Autoregressive Model

Large Language Diffusion Models (LLDMs) are emerging as an alternative to autoregressive models, offering faster inference through higher parallelism. Similar to autoregressive LLMs, they remain prone to hallucinations, making reliable uncertainty quantification (UQ) crucial for safe deployment. However, existing UQ methods are fundamentally misaligned with this new paradigm: they assume autoregressive factorization or use expensive repeated sampling, negating the efficiency of LLDMs. In this work, we present the first systematic study of UQ for LLDMs and propose lightweight, zero-shot uncertainty signals derived from the iterative denoising process, leveraging intermediate generations, token remasking dynamics, and denoising complexity. We further adapt a state-of-the-art UQ method to LLDMs by combining masked diffusion likelihoods with trajectory-based semantic dissimilarity. We prove that expected trajectory dissimilarity lower bounds the masked diffusion training objective, which motivates its usage as an uncertainty score. Comprehensive experiments across three tasks, eight datasets, and two models show that our method achieves a great cost-performance trade-off: it approaches the strongest sampling-based baselines while incurring up to 100x lower computational overhead. Our work demonstrates that LLDMs can deliver both fast inference and reliable hallucination detection simultaneously.

This work reformulates language generation as a stochastic optimal control problem, providing a unified theoretical perspective to analyze autoregressive and diffusion models and explain their limitations (Efficiency-Fidelity Paradox, Irreversibility Error Propagation, Optimization Tractability and Fidelity) in terms of combination of trajectory singularity, adjoint state vanishing, and gradient absence. To address these issues, we approximate the solution to the Hamilton-Jacobi-Bellman (HJB) equation, yielding an optimal policy that acts as a closed-loop controller. To bypass the intractability of directly solving the HJB PDE, we employ Flow Matching as the optimal trajectory solver within the rectified latent control space. This allows our Manta-LM with Global Integral Operator to approximate the global vector field, effectively realizing a model that simultaneously achieves high-fidelity text generation and efficient, low-cost parallel sampling. Empirically, our method achieves strong performance on language modeling and conditional generation tasks, while exhibiting improved stability, efficiency, and controllability.

Continuous diffusion language models lag behind autoregressive transformers, partly because diffusion is applied in spaces poorly suited to language denoising and token recovery. We propose DiHAL, a geometry-guided diffusion-transformer hybrid that asks where diffusion should enter a pretrained transformer. DiHAL scores layers with geometry-based proxies, selects a diffusion-friendly hidden-state interface, and replaces the lower transformer prefix with a diffusion bridge while retaining the upper layers and original LM head. By reconstructing the selected-layer hidden state rather than tokens, DiHAL avoids direct continuous-to-discrete recovery. Experiments on 8B-scale backbones show that the geometry score predicts effective shallow insertion layers under a fixed bridge-training protocol and that hidden-state recovery improves over continuous diffusion baselines in a diagnostic comparison matching the diffusion/recovery training budget. These results suggest that hidden-state geometry helps identify where diffusion-based replacement is feasible inside pretrained language models.

Discrete diffusion language models improve generation efficiency through parallel token prediction, but standard $X_0$ prediction methods introduce factorization errors by approximating the clean token posterior with independent token-wise distributions. This paper proposes Factorization-Error-Free Discrete Diffusion Language Modeling (FeF-DLLM), which replaces independent clean-token prediction with an exact prefix-conditioned factorization of the clean posterior to better preserve token dependencies. To reduce the sequential cost introduced by prefix conditioning, FeF-DLLM further incorporates speculative decoding within diffusion denoising, accelerating inference while maintaining the parallel prediction and re-masking properties of DLLMs. Theoretically, we prove that FeF-DLLM generates from the true joint distribution and derive its expected acceleration ratio. Experiments on GSM8K, MATH, HumanEval, and MBPP demonstrate that our method improves accuracy by an average of 5.04 percentage points while achieving an average inference speedup of $3.86\times$.

Under modern test-time compute and agentic paradigms, language models process ever-longer sequences. Efficient text generation with transformer architectures is increasingly constrained by the Key-Value cache memory footprint and bandwidth. To address this limitation, we introduce Self-Pruned Key-Value Attention (SP-KV), a mechanism designed to predict future KV utility in order to reduce the size of the long-term KV cache. This strategy operates at a fine granularity: a lightweight utility predictor scores each key-value pair, and while recent KVs are always available via a local window, older pairs are written in the cache and used in global attention only if their predicted utility surpasses a given threshold. The LLM and the utility predictor are trained jointly end-to-end exclusively through next-token prediction loss, and are adapted from pretrained LLM checkpoints. Rather than enforcing a fixed compression ratio, SP-KV performs dynamic sparsification: the mechanism adapts to the input and typically reduces the KV cache size by a factor of $3$ to $10\times$, longer sequences often being more compressible. This leads to vast improvements in memory usage and decoding speed, with little to no degradation of validation loss nor performance on a broad set of downstream tasks. Beyond serving as an effective KV-cache reduction mechanism, our method reveals structured layer- and head-specific sparsity patterns that we can use to guide the design of hybrid local-global attention architectures.

Generative models are often trained with a next-token prediction objective, yet many downstream applications require the ability to estimate or control sequence-level properties. Next-token prediction can lead to overfitting of local patterns during training, underfitting of global structure, and requires significant downstream modifications or expensive sampling to guide or predict the global attributes of generated samples at inference time. Here, we introduce Conditional Attribute Transformers, a novel method for jointly estimating the next-token probability and the value of an attribute conditional on each potential next token selection. This framework enables three critical capabilities within a single forward pass, without modification of the input sequence: (1) per-token credit assignment across an entire sequence, by identifying how each token in a sequence is associated with an attribute's value; (2) counterfactual analysis, by quantifying attribute differences conditional on alternative next token choices; (3) steerable generation, by decoding sequences based on a combination of next-token and attribute likelihoods. Our approach achieves state of the art performance on sparse reward tasks, improves next-token prediction at sufficient model sizes, estimates attribute probabilities orders of magnitude faster than sampling, and can guide decoding of autoregressive sequence models on a range of language tasks.

Discrete diffusion models are increasingly competitive for language modeling, yet it remains unclear how their denoising objectives organize learning. Although these objectives target the full data distribution, we show that the exact reverse process induces a hierarchy between coarse support information and finer frequency information. For uniform and absorbing (a.k.a. masking) diffusion, we prove that, in the small-noise regime of the final denoising steps, each single-token reverse edit decomposes into a leading scale, determined by whether it moves toward the data support (e.g., grammatically valid sentences), and a finer coefficient, determining relative probabilities within the same scale. Thus, recovering validity structure only requires learning the correct order of magnitude of reverse probabilities, whereas recovering data frequencies requires coefficient-level estimation. The separation is mechanism-dependent: uniform diffusion exhibits a trichotomy into validity-improving, validity-preserving, and validity-worsening edits, while absorbing diffusion places its leading-order mass on validity-improving moves. Experiments on a masked language diffusion model and synthetic regular-language tasks support these predictions: support-localization emerges earlier than within-support frequency ranking, and the contrast between uniform and absorbing diffusion matches the predicted rate separation. Together, our results suggest that discrete diffusion models learn data support before data frequencies.

Diffusion language models are a promising alternative to autoregressive models, yet post-training methods for them largely adapt reward-maximizing objectives. We identify a central failure mode in this setting we call trajectory locking: sampled reward-driven updates over-concentrate probability mass onto a narrow set of denoising paths, reducing coverage of alternative correct solutions under repeated sampling. To address this, we propose TraFL (Trajectory Flow baLancing), a trajectory-balance objective that trains the policy toward a reward-tilted target distribution anchored to a frozen reference model. We make this practical for diffusion language models with a diffusion-compatible sequence-level surrogate and a learned prompt-dependent normalization. Across mathematical reasoning and code generation benchmarks, TraFL is the only evaluated post-training method that improves over the base model in every benchmark-length setting, with gains that persist as the sampling budget increases. The improvements transfer to held-out evaluations: TraFL stays above the base model on Minerva Math and is the strongest method on every LiveCodeBench difficulty split.

We introduce a family of synthetic languages with hierarchical structure -- generated by a broadcast process on trees -- for which the role of context length and reasoning in autoregressive generation can be analyzed precisely. At the heart of our analytic approach is an \emph{exact $k$-gram ansatz} in place of transformers with context length $k$, a substitution we then validate empirically. Using this ansatz we derive explicit asymptotic predictions for distributional statistics of the sequences produced by a trained model, instantiated in two settings. For the \emph{Ising broadcast process} (a soft-constrained language), we prove that the variance of the generated sum scales log-linearly in the context depth and its kurtosis converges to that of a Gaussian -- both deviating from the true language for any sublinear context. For the \emph{coloring broadcast process} (a hard-constrained language) in the freezing regime, bounded-context autoregression produces sequences that, with high probability, are inconsistent with \emph{any} valid coloring of the underlying tree. Together these results imply an $Ω(n)$ lower bound on the context length required to faithfully sample length-$n$ sequences. In contrast, we prove that an autoregressive \emph{reasoning} model with only $Θ(\log n)$ working memory can sample exactly from the true language -- an exponential improvement. We confirm both the lower-bound predictions and the reasoning-based upper bound empirically with transformers trained on the synthetic language; the trained models track our asymptotic predictions quantitatively across a wide range of context sizes.

Flow Language Models (FLMs) are a recently introduced class of language models which adapt continuous flow matching for one-hot encoded token sequences. Their denoisers have a special structure absent from generic continuous diffusion models: each block of the denoising mean is a posterior marginal distribution over the clean token at that position. Standard DDPM-style samplers collapse these marginals to a single conditional-mean endpoint and bridge toward this simplex-valued point, which is generally not a valid one-hot sequence. We argue that the natural sampler for an FLM is instead posterior-predictive. At each reverse step, we sample a clean one-hot endpoint from the factorized posterior defined by the FLM token marginals, and then sample the next continuous state from the analytic Ornstein--Uhlenbeck bridge conditioned on that endpoint. The method is training-free, uses the same model evaluations as standard sampling, and gives a principled interface for token-level decoding controls such as temperature scaling and nucleus truncation. We show that, under exact posterior marginals, the endpoint approximation error is exactly the conditional multi-information among token positions. The induced one-step bridge kernel preserves all token-wise posterior-predictive marginals and loses only the residual cross-position dependence. Finally, we prove a Girsanov path-space comparison showing that the marginal-conditioned bridge has a no-larger denoising-error term than the frozen conditional-mean bridge, with strict improvement whenever intermediate coordinate-wise bridge observations reveal additional information about the clean token. Experiments with FLMs show that the sampler improves the quality--diversity tradeoff. Code is available at: github.com/imbirik/mcb.

While autoregressive (AR) Vision-Language-Action (VLA) models have demonstrated formidable reasoning capabilities in robotic tasks, their sequential decoding process often incurs high inference latency and may amplify error accumulation during long-horizon execution. Discrete Diffusion Language Models (dLLMs) provide a promising alternative through parallel token refinement, but their practical deployment in robotics remains limited by repeated denoising function evaluations (NFEs) and the difficulty of directly applying standard KV caching to bidirectional iterative decoding. To bridge these paradigms, we propose BlockVLA, a framework that adapts pretrained AR backbones into an efficient discrete diffusion policy through a block diffusion paradigm. BlockVLA maintains autoregressive dependencies at the block level while enabling parallel denoising within each block, thereby combining global causal coherence with local parallel generation. This design enables prefix KV-cache reuse across completed blocks, reduces the effective cost of iterative denoising, and provides a smoother transition from AR pretraining to diffusion-based policy fine-tuning. We conduct extensive evaluations on the LIBERO and SimplerEnv benchmarks. Experimental results demonstrate that our BlockVLA achieves a 3.3$\times$ inference acceleration over standard discrete diffusion baselines. Furthermore, our model exhibits superior training efficiency, with success rates converging substantially faster than baselines, a gain that is particularly pronounced in complex, long-horizon tasks, where BlockVLA achieves significant performance gains in the early stages of training. This work establishes Block Diffusion as a robust bridge between large-scale pretrained AR models and efficient, high-frequency real-time robotic control.

While EEG foundation models have shown significant potential in universal neural decoding across tasks, their advancement remains constrained by the inadequacy modeling of complex spatiotemporal topology, as well as the inherent modality gap between low-level physiological signals and high-level textual semantics. To address these challenges, we propose a Knowledge-Anchored Semantically-Dynamic Topology Brain Autoregressive Model (KAST-BAR), which dynamically aligns physiological representations derived from multi-level brain topology with an expert-level semantic space. Specifically, we design a Dual-Stream Hierarchical Attention (DSHA) encoder that accurately captures the brain's intrinsic non-Euclidean topology by modeling local temporal dynamics with global spatial contexts. On this basis, a Knowledge-Anchored Semantic Profiler (KASP) is proposed to synthesize physically-grounded and instance-level textual profiles, which subsequently drive a Semantic Text-Aware Refiner (STAR) to dynamically reconstruct EEG representations using Latent Expert Queries. By conducting large-scale pre-training on 21 diverse datasets to build a foundation model, KAST-BAR effectively integrates expert-level medical knowledge into EEG signal representations, consistently achieving superior performance across six downstream tasks. Our code is available at https://github.com/KAST-BAR/KAST-BAR

Diffusion Language Models (DLMs) provide a promising alternative to autoregressive language models by generating text through iterative denoising and bidirectional refinement. However, this iterative generation paradigm also introduces unique safety vulnerabilities when harmful tokens generated at intermediate denoising steps propagate through subsequent refinement processes and eventually induce unsafe outputs. While there are a few attempts to remedy this issue, they either fail to generate safe outputs or generate safe yet low-quality outputs. This motivates us to propose an inference-time defense framework based on the step-wise intervention during the denoising process, which then improves the safety without compromising the output quality. The key component of our framework is a contrastive safety direction (SGD), a latent direction that captures the semantic boundary between harmful and safe generations. We leverage SGD to assess the alignment of generated tokens with harmful semantics at each denoising step. When harmful alignment is detected, our method remasks the corresponding tokens and resumes the denoising process with adaptive steering, where the steering strength is modulated according to the estimated degree of harmfulness. As a plug-and-play module, our method circumvents the need for additional fine-tuning and can be directly incorporated into off-the-shelf diffusion models. The experimental results show that our approaches reduce jailbreak success rates to 0.64% while preserving generation quality close to the original model performance. This confirms the effectiveness of step-wise intervention for safe diffusion language model generation. Our code is available at https://github.com/leeyejin1231/DLM_Steering_Remasking.

Masked diffusion models (MDMs) have emerged as a promising alternative to autoregressive models (ARMs) for language modeling. However, MDMs are known to learn substantially more slowly than ARMs, which may become problematic when scaling MDMs to larger models. Therefore, we ask the following question: how can we accelerate standard MDM training while maintaining its final performance? To this end, we first provide a detailed analysis of why MDM training is slow. We find that the main factor is the locality bias of language: the predictive information for a token is concentrated in nearby positions. We further investigate how this bias slows learning and suggest a simple yet effective remedy: bell-shaped time sampling as a training strategy. Notably, MDMs trained with our training recipe reach the same validation negative log-likelihood (NLL) up to $\sim4\times$ faster than standard training on One Billion Word Benchmark (LM1B). We also show faster improvements in generative perplexity, zero-shot perplexity, and downstream task performance on various benchmarks.

Neural population models, which predict the joint firing of many simultaneously recorded neurons forward in time, are typically evaluated by a single aggregate Pearson correlation $r$ between predicted and actual spike counts, a number that masks critical structure. We argue that how we evaluate spike forecasting matters as much as what we build, and introduce SpikeProphecy, the first large-scale benchmark for causal, autoregressive spike-count forecasting on real electrophysiology recordings. Our core contribution is a population metric decomposition that separates aggregate performance into temporal fidelity, spatial pattern accuracy, and magnitude-invariant alignment. The decomposition surfaces aspects of the underlying data that an aggregate scalar collapses together. We apply the protocol to 105 Neuropixels sessions (Steinmetz 2019 + IBL Repeated Site; ~89,800 neurons) with seven architecture baselines spanning four structural families: four SSMs (three diagonal and one non-diagonal), a Transformer, an LSTM, and a spiking network. The decomposition surfaces a brain-region predictability ranking that reproduces across all seven baselines and survives ANCOVA correction for firing-statistics constraints (region $ΔR^2 = 0.018$ above the firing-statistics covariates). It also exposes a sub-Poisson evaluation floor where rigorous metrics combine with genuine biophysical constraints on regular spike trains, and yields a negative result on KL-on-output-rates distillation for ANN-to-SNN transfer in this Poisson count domain.

Probabilistic Circuits (PCs) are deep generative models that support exact and efficient probabilistic inference. Yet in autoregressive language modeling, PCs still lag behind Transformer-based large language models (LLMs), suggesting an important expressivity gap. In this work, we compare PCs and LLMs under a unified autoregressive formulation. First, an output bottleneck: PCs parameterize predictions as convex combinations in probability space, which struggles to represent the sharp distributions typical of language; adopting a logit-space parameterization substantially narrows this gap. Second, a context-encoding bottleneck: we prove that structured-decomposable PCs can match Transformer separation rank on vtree-aligned partitions, but show, both theoretically and empirically, that this capacity is limited to partitions aligned with the fixed routing structure, leading to severe degradation when the data exhibits heterogeneous dependency topologies. We further prove that decomposable PCs are strictly more expressive than structured-decomposable ones, though effectively optimizing them remains an open challenge.

Continuous diffusion is a natural framework for non-autoregressive generation but has generally lagged behind masked discrete diffusion models (MDMs) on discrete sequence generation. We argue that the bottleneck is not continuity itself, but a representation in which denoising depends on timestep-indexed noise regimes. We introduce \emph{Discrete Stochastic Localization} (DSL), a continuous-state framework with unit-sphere token embeddings whose Bayes-optimal denoiser is invariant to the nominal signal-to-noise ratio (SNR) under the localization channel. One trained network then supports an entire family of per-token SNR paths, with endpoint masked-diffusion paths as a special case. Fine-tuning a pretrained MDLM checkpoint with DSL substantially improves distributional faithfulness (MAUVE) on OpenWebText across all step budgets from $T{=}128$ to $T{=}1024$, and the same checkpoint supports random-order autoregressive sampling, as well as a hybrid continuous-then-discrete sampler using as few as T=48 total steps -- without distillation or retraining.

We introduce Orthrus, a simple and efficient dual-architecture framework that unifies the exact generation fidelity of autoregressive Large Language Models (LLMs) with the high-speed parallel token generation of diffusion models. The sequential nature of standard autoregressive decoding represents a fundamental bottleneck for high-throughput inference. While diffusion language models attempt to break this barrier via parallel generation, they suffer from significant performance degradation, high training costs, and a lack of rigorous convergence guarantees. Orthrus resolves this dichotomy natively. Designed to seamlessly integrate into existing Transformers, the framework augments a frozen LLM with a lightweight, trainable module to create a parallel diffusion view alongside the standard autoregressive view. In this unified system, both views attend to the exact same high-fidelity Key-Value (KV) cache; the autoregressive head executes context pre-filling to construct accurate KV representations, while the diffusion head executes parallel generation. By employing an exact consensus mechanism between the two views, Orthrus guarantees lossless inference, delivering up to a 7.8x speedup with only an O(1) memory cache overhead and minimal parameter additions.

This paper introduces a physics-informed generative framework that resolves the fundamental conflict between the statistical flexibility of deep learning and the rigorous theoretical constraints of fixed-income modeling. We demonstrate that standard generative models and unconstrained statistical extrapolations suffer from "manifold collapse" and severe arbitrage violations when forecasting term structures across diverse macroeconomic regimes. To overcome this, we propose a two-stage architecture. First, a Student-t Conditional Variational Autoencoder with Dynamic Level Injection (CVAEsT+LS) extracts a robust, heavy-tailed term structure manifold, effectively decoupling macroeconomic shape dynamics from absolute base rates. Second, the latent dynamic evolution is governed by a continuous-time Neural Stochastic Differential Equation (SDE) strictly penalized by a No-Arbitrage Partial Differential Equation (PDE). Empirical results across multiple sovereign currencies (USD, GBP, JPY) confirm that our synergistic approach drastically reduces out-of-sample forecasting errors -- achieving an exceptional 6.58 bps Mean Tenor RMSE -- and successfully overcomes the massive parallel drift and zero-lower-bound violations exhibited by the classical HJM model in extreme environments. Furthermore, through phase space vector field analysis, we demonstrate the model's superior capability in unsupervised macroeconomic regime detection and high-quality continuous-time scenario generation. Ultimately, this research provides a highly scalable, mathematically sound evolutionary engine for term structure modeling.

Autoregressive video generation aims at real-time, open-ended synthesis. Yet, cinematic storytelling is not merely the endless extension of a single scene; it requires progressing through evolving events, viewpoint shifts, and discrete shot boundaries. Existing autoregressive models often struggle in this setting. Trained primarily for short-horizon continuation, they treat long sequences as extended single shots, inevitably suffering from motion stagnation and semantic drift during long rollouts. To bridge this gap, we introduce CausalCine, an interactive autoregressive framework that transforms multi-shot video generation into an online directing process. CausalCine generates causally across shot changes, accepts dynamic prompts on the fly, and reuses context without regenerating previous shots. To achieve this, we first train a causal base model on native multi-shot sequences to learn complex shot transitions prior to acceleration. We then propose Content-Aware Memory Routing (CAMR), which dynamically retrieves historical KV entries according to attention-based relevance scores rather than temporal proximity, preserving cross-shot coherence under bounded active memory. Finally, we distill the causal base model into a few-step generator for real-time interactive generation. Extensive experiments demonstrate that CausalCine significantly outperforms autoregressive baselines and approaches the capability of bidirectional models while unlocking the streaming interactivity of causal generation. Demo available at https://yihao-meng.github.io/CausalCine/

We study the fundamental and timely problem of learning long sequences in autoregressive modeling and next-token prediction under model misspecification, measured by the joint Kullback--Leibler (KL) divergence. Our goal is to characterize how the sequence horizon $H$ affects both approximation and estimation errors in this joint-distribution, sequence-level regime. By establishing matching upper and lower bounds, we provide, to our knowledge, the first complete characterization of long-horizon error behavior under the natural joint KL objective, with improved rates and optimality justification relative to existing work. On the approximation side, we show that joint KL admits a horizon-free approximation factor, in sharp contrast to Hellinger-based analyses that exhibit an $Ω(H)$ dependence for computationally efficient methods; this isolates the choice of divergence as the source of approximation amplification. On the estimation side, we prove a fundamental information-theoretic lower bound of order $Ω(H)$ that holds for both decomposable policy classes and fully shared policies, matching the $\widetilde O(H)$ upper bounds achieved by computationally efficient algorithms. Our analysis clarifies the landscape of recent autoregressive learning results by aligning the log-loss training objective, the sequence-level evaluation metric, and the approximation metric {\color{black}through a sharp joint-KL oracle theory}. We further show that these joint-KL guarantees imply policy learning regret bounds at rates matching prior imitation learning literature.

Generating realistic and user-preferred advertisements is a key challenge in e-commerce. Existing approaches utilize multiple independent models driven by click-through-rate (CTR) to controllably create attractive image or text advertisements. However, their pipelines lack cross-modal perception and rely on CTR that only reflects average preferences. Therefore, we explore jointly generating personalized image-text advertisements from historical click behaviors. We first design a Unified Advertisement Generative model (Uni-AdGen) that employs a single autoregressive framework to produce both advertising images and texts. By incorporating a foreground perception module and instruction tuning, Uni-AdGen enhances the realism of the generated content. To further personalize advertisements, we equip Uni-AdGen with a coarse-to-fine preference understanding module that effectively captures user interests from noisy multimodal historical behaviors to drive personalized generation. Additionally, we construct the first large-scale Personalized Advertising image-text dataset (PAd1M) and introduce a Product Background Similarity (PBS) metric to facilitate training and evaluation. Extensive experiments show that our method outperforms baselines in general and personalized advertisement generation. Our project is available at https://github.com/JD-GenX/Uni-AdGen.

Diffusion Language Models (DLMs) generate text by iteratively denoising masked token sequences, offering a tradeoff between parallelism and quality compared to autoregressive models. In current practice, the number of tokens decoded per step is controlled by a confidence threshold, and quality degrades monotonically as more tokens are denoised per step. We introduce Multi-token Residual Prediction (MRP), a lightweight module that enables dependency-aware multi-token denoising within a single backbone forward pass. MRP exploits a key property of the denoising process: the logit distributions at adjacent denoising steps are remarkably similar. Rather than running the backbone a second time to obtain the next-step logits, MRP predicts the residual between steps from the backbone's hidden states, effectively denoising more tokens per backbone forward at a fraction of the cost. We apply MRP across the two operating regimes of DLM decoding. In the high-quality-low-throughput static denoising regime, MRP serves as a drafter for speculative decoding: its proposals are verified against the backbone, yielding lossless acceleration of up to 1.4x in SGLang. In the low-quality-high-throughput dynamic denoising regime, MRP instead drives a remasking scheme that revokes over-eager reveals, recovering most of the accuracy lost to aggressive low-threshold decoding and improving accuracy by up to 22.6 points on code generation task HumanEval and 17.7 points on reasoning task GSM8K.

Diffusion Language Models (DLMs) have recently emerged as a promising alternative to autoregressive language models, offering stronger global awareness and highly parallel generation. However, post-training DLMs with standard Negative Evidence Lower Bound (NELBO)-based supervised fine-tuning remains inefficient: training reconstructs randomly masked tokens in a single step, whereas inference follows a confidence-guided, multi-step easy-to-hard denoising trajectory. Recent trajectory-based self-distillation methods exploit such inference trajectories mainly for sampling-step compression and acceleration, often improving decoding efficiency without substantially enhancing the model's underlying capability, and may even degrade performance under full diffusion decoding. In this work, we ask whether self-distilled trajectories can be used not merely for faster inference, but for genuine knowledge acquisition. Although these trajectories lie on the pretrained DLM's own distributional manifold and thus offer a potentially lower optimization barrier, we find that naively fine-tuning on them with standard NELBO objectives yields only marginal gains. To address this limitation, we propose \textbf{T}rajectory-\textbf{A}ligned optimization via \textbf{Bo}ltzmann \textbf{M}odeling (\textbf{TABOM}), a self-distilled trajectory-based post-training framework that aligns training with the easy-to-hard structure of inference. TABOM models the inference unmasking preference as a Boltzmann distribution over predictive entropies and derives a tractable pairwise ranking objective to align the model's certainty ordering with the observed decoding trajectory. Empirically, TABOM achieves substantial gains in new domains, expands the effective knowledge boundary of DLMs, and significantly mitigates catastrophic forgetting compared with standard SFT.

By processing electronic health records (EHRs) as natural language sequences, large language models (LLMs) have shown potential in clinical prediction tasks such as mortality prediction and phenotyping. However, longitudinal or highly frequent EHRs often yield excessively long token sequences that result in high computational costs and even reduced performance. Existing solutions either add modules for compression or remove less important tokens, which introduce additional inference latency or risk losing clinical information. To achieve lossless compression of token sequences without additional cost or loss of performance, we propose Medical Token-Pair Encoding (MedTPE), a layered method that extends standard tokenisation for EHR sequences. MedTPE merges frequently co-occurring medical token pairs into composite tokens, providing lossless compression while preserving the computational complexity through a dependency-aware replacement strategy. Only the embeddings of the newly introduced tokens of merely 0.5-1.0% of the LLM's parameters are fine-tuned via self-supervised learning. Experiments on real-world datasets for two clinical scenarios demonstrate that MedTPE reduces input token length by up to 31% and inference latency by 34-63%, while maintaining or even improving both predictive performance and output format compliance across multiple LLMs and four clinical prediction tasks. Furthermore, MedTPE demonstrates robustness across different input context lengths and generalisability to scientific and financial domains and different languages.

Recently, reinforcement learning (RL) has been widely applied during post-training for diffusion large language models (dLLMs) to enhance reasoning with block-wise semi-autoregressive generation. Block size has therefore become a vital factor in dLLMs, since it determines the parallel decoding granularity and affects the rollout trajectories during RL optimisation, e.g., GRPO. Instead of investigating the effect of block size during inference on individual domains, this paper studies block size from a domain conflict perspective for dLLM RL post-training in multi-domain scenarios. The main contributions are: (1) a formulation of domain block size conflict in multi-domain RL for dLLMs, which will largely affect the post-training effectiveness for rollout-based RL methods; (2) a novel dataset, Block-R1-41K is constructed with a best-improved training block size for each sample, which also induces a Block Size Conflict Score to quantitatively measure the domain conflict; (3) a new benchmark, Block-R1, for flexible RL post-training for dLLMs in both single and cross domain; and (4) a simple yet powerful cross-domain post-training method with sample-level best-improved training block sizes. Extensive experiments on 13 distinct datasets, 7 latest RL algorithms and diverse dLLM backbones are comprehensively covered in Block-R1. The benchmark is open-sourced at https://github.com/YanJiangJerry/Block-R1 with the dataset released at https://huggingface.co/datasets/YanJiangJerry/Block-R1-41K.

We present ScaleMoGen, a scale-wise autoregressive framework for text-driven human motion generation. Unlike conventional autoregressive approaches that rely on standard next-token prediction, ScaleMoGen frames motion generation as a coarse-to-fine process. We quantize 3D motions into compositional discrete tokens across multiple skeletal-emporal scales of increasing granularity, learning to generate motion by autoregressively predicting next-scale token maps. To maintain structural integrity, our motion tokenizers and quantizers are explicitly designed so that discrete tokens at every scale strictly preserve the skeletal hierarchy. Additionally, we employ bitwise quantization and prediction, which efficiently scale up the tokenizer vocabulary to preserve motion details and stabilize optimization. Extensive experiments demonstrate that ScaleMoGen achieves state-of-the-art performance, establishing an FID of 0.030 (vs. 0.045 for MoMask) on HumanML3D and a CLIP Score of 0.693 (vs. 0.685 for MoMask++) on the SnapMoGen dataset. Furthermore, we demonstrate that our skeletal-temporal multi-scale representation naturally facilitates training-free, text-guided motion editing.

Closed-loop driving simulation requires real-time interaction beyond short offline clips, pushing current driving world models toward autoregressive (AR) rollout. Existing AR distillation approaches typically rely on frame sinks or student-side degradation training. The former transfers poorly to driving due to fast ego-motion and rapid scene changes, while the latter remains bounded by the teacher's single-pass output length and thus provides only a limited supervision horizon. A natural question is: can the teacher itself be extended via AR rollout to provide unbounded-horizon supervision at bounded memory cost? The key difficulty is that a standard teacher drifts under its own predictions, contaminating the supervision it provides. Our key insight is to make the teacher rollout-capable, ensuring reliable supervision from its own AR rollouts. This is instantiated as HorizonDrive, an anti-drifting training-and-distillation framework for AR driving simulation. First, scheduled rollout recovery (SRR) trains the base model to reconstruct ground-truth future clips from prediction-corrupted histories, yielding a teacher that remains stable across long AR rollouts. Second, the rollout-capable teacher is extended via AR rollout, providing long-horizon distribution-matching supervision under bounded memory, while a short-window student aligns to it with teacher rollout DMD (TRD) for efficient real-time deployment. HorizonDrive natively supports minute-scale AR rollout under bounded memory; on nuScenes, HorizonDrive reduces FID by 52% and FVD by 37%, and lowers ARE and DTW by 21% and 9% relative to the strongest long-horizon streaming baselines, while remaining competitive with single-pass driving video generators.

Autoregressive language models generate text one token at a time, yet natural language is inherently structured in multi-token units, including phrases, n-grams, and collocations that carry meaning jointly. This one-token bottleneck limits both the expressiveness of the model during pre-training and its throughput at inference time. Existing remedies such as speculative decoding or diffusion-based language models either leave the underlying bottleneck intact or sacrifice the causal structure essential to language modeling. We propose BitLM, a language model that represents each token as a fixed-length binary code and employs a lightweight diffusion head to denoise multiple tokens in parallel within each block. Crucially, BitLM preserves left-to-right causal attention across blocks while making joint lexical decisions within each block, combining the reliability of autoregressive modeling with the parallelism of iterative refinement. By replacing the large-vocabulary softmax with bitwise denoising, BitLM reframes token generation as iterative commitment in a compact binary space, enabling more efficient pre-training and substantially faster inference without altering the causal foundation that makes language models effective. Our results demonstrate that the one-token-at-a-time paradigm is not a fundamental requirement but an interface choice, and that changing it can yield a stronger and faster language model. We hope BitLM points toward a promising direction for next-generation language model architectures.

Generative recommendation (GR) has emerged as a promising paradigm that predicts target items by autoregressively generating their semantic identifiers (SID). Most GR methods follow a quantization-representation-generation pipeline, first assigning each item a SID, then constructing input representations from SID-token embeddings, and finally predicting the target SID through autoregressive generation. Existing item-level representation constructions mainly take two forms: directly merging SID-token embeddings into a compact vector, or enriching item-level representations with external inputs through additional networks. However, these item-level constructors still expose two practical challenges: direct merging may amplify the information loss caused by quantization and ID collision while obscuring SID code relations, whereas external-input-based methods can strengthen item semantics but cannot reliably preserve the SID-structured evidence required for token-level generation. These limitations make representation construction an underexplored bottleneck, leading to two severe problems, \ie{} the Identity-Structure Preservation Conflict and Input-Output Granularity Mismatch. To this end, we propose ComeIR, a Conditional Memory enhanced Item Representation framework that reconstructs SID-token embeddings into item-aware inputs and restores the token granularity during SID decoding. Specifically, MM-guided token scoring adaptively estimates the contribution of each code within the SID, dual-level Engram memory captures intra-item code composition and inter-item transition patterns, and a memory-restoring prediction head reuses the memories during SID decoding. Extensive experiments demonstrate the effectiveness and flexibility of ComeIR, and further reveal scalable gains from enlarging conditional memory.

Learning transferable representations for electroencephalography (EEG) remains challenging because EEG signals are inherently multi-channel and non-stationary. Channels observed at the same time provide coupled measurements of neural activity, while the relevant temporal dynamics vary across contexts. This structure is poorly matched by architectures that apply uniform computation across time or route each channel patch independently. To this end, we propose TRACE, an autoregressive EEG pre-training framework that predicts future EEG patches from causal context while performing temporally adaptive and cross-channel coherent computation. At each temporal step, TRACE derives an expert routing decision from the causal cross-channel history and applies it jointly to all channels at that step. This preserves instantaneous cross-channel coherence while allowing different temporal regimes to activate different computation. Since routing is defined over the available channel set and causal temporal context, TRACE is compatible with heterogeneous pre-training across corpora with different channel counts, montages, sequence lengths, and recording domains. Across eight downstream EEG benchmarks, TRACE is evaluated in both settings: when downstream domains are seen only as unlabeled pre-training data and when downstream datasets are completely unseen during pre-training. It obtains the best results on several benchmarks while remaining competitive on motor imagery and clinical event classification tasks, with ablations supporting the importance of cross-channel temporal routing.

Discrete Diffusion Language Models progressed rapidly as an alternative to autoregressive (AR) models, motivated by their parallel generation abilities. However, for tractability, discrete diffusion models sample from a factorized distribution, which is less expressive than AR. Recent Flow Language Models (FLMs) apply continuous flows to language, transporting noise to data with a deterministic ODE that avoids factorized sampling. FLMs operate on one-hot vectors whose dimension scales with the vocabulary size, making FLMs costly to train. Moreover, since all distinct one-hot embeddings are equidistant in $\ell_2$, adding Gaussian noise does not have a clear semantic interpretation (unlike images, where Gaussian noise progressively degrades structure). We introduce $\mathbb{S}$-FLM, a latent FLM in the hypersphere. $\mathbb{S}$-FLM generates sequences by rotating vectors in $\mathbb{S}^{d-1}$ along a velocity field learned with cross-entropy, avoiding the overhead of materializing one-hot vectors. Previous FLMs match AR in Generative Perplexity (Gen.\ PPL), but samples with high likelihood are not necessarily correct in verifiable domains such as math and code. $\mathbb{S}$-FLM substantially improves continuous flow language models on large-vocabulary reasoning and closes the gap to masked diffusion under standard-temperature sampling ($T=1$), while a gap remains under optimized low-temperature ($T=0.1$) decoding.

Diffusion and flow-based models have become the de facto approaches for generating continuous data, e.g., in domains such as images and videos. Their success has attracted growing interest in applying them to language modeling. Unlike their image-domain counterparts, today's leading diffusion language models (DLMs) primarily operate over discrete tokens. In this paper, we show that continuous DLMs can be made effective with minimal adaptation to the discrete domain. We propose Embedded Language Flows (ELF), a class of diffusion models in continuous embedding space based on continuous-time Flow Matching. Unlike existing DLMs, ELF predominantly stays within the continuous embedding space until the final time step, where it maps to discrete tokens using a shared-weight network. This formulation makes it straightforward to adapt established techniques from image-domain diffusion models, e.g., classifier-free guidance (CFG). Experiments show that ELF substantially outperforms leading discrete and continuous DLMs, achieving better generation quality with fewer sampling steps. These results suggest that ELF offers a promising path toward effective continuous DLMs.

We introduce an automatically generated benchmark for predicting hidden text in technical papers. A paper supplies visible context $X$ and a hidden continuation $Y$; the evaluated model writes an auxiliary forecast string $Z$, and a separate scorer assigns next-token probability to $Y$ both with and without conditioning on $Z$. This gives a label-free test of whether $Z$ transmits information about the continuation, compared against controls where $Z$ is recent context rather than a forecast. Our main testbed is equation-suffix prediction: the predictor sees context and the first part of a displayed equation, then forecasts the rest. The task mixes surface-level arXiv/TeX text modeling with reasoning-sensitive inference; the suffix is one of many roughly equivalent continuations, so the benchmark is read statistically rather than item-by-item. On 1363 equation continuations from 138 recent physics and mathematics papers, forecasts from GPT-5.5, Opus 4.7, and GPT-5.4 nano all improve clipped likelihood over the context control under both Qwen3-8B and Kimi K2.6 scorers, distinguishing model families and reasoning-effort settings without human labels. To emulate shortcuts where $Z$ further primes the scorer rather than making a useful forecast, we also fine-tune the scorer on context-only prompts and apply it to held-out papers as a stronger control. GPT-5.5 forecasts still beat this fine-tuned control; GPT-5.4 nano forecasts do not. Longer prose/TeX continuations show positive but noisier lift over controls, concentrated near the beginning of the target. These results support cross-model likelihood scoring as a static benchmark and as a setup for probing shortcut vulnerabilities before reinforcement learning or model-selection optimization is applied.

Masked Diffusion Models (MDMs) have emerged as a promising alternative to autoregressive models in language modeling, offering the advantages of parallel decoding and bidirectional context processing within a simple yet effective framework. Specifically, their explicit distinction between masked tokens and data underlies their simple framework and effective conditional generation. However, MDMs typically require many sampling iterations due to factorization errors stemming from simultaneous token updates. We observe that a theoretical lower bound of the factorization error exists, which standard MDMs cannot reduce due to their use of a deterministic single-state mask. In this paper, we propose the Infinite Mask Diffusion Model (IMDM), which introduces a stochastic infinite-state mask to mitigate the theoretical bound while directly inheriting the benefits of MDMs, including the compatibility with pre-trained weights. We empirically demonstrate that MDM fails to perform few-step generation even in a simple synthetic task due to the factorization error bound, whereas IMDM can find an efficient solution for the same task. Finally, when equipped with appropriate distillation methods, IMDM surpasses existing few-step distillation methods at small step counts on LM1B and OpenWebText. Code is available at https://Ugness.github.io/official_imdm.

Large language models (LLMs) exhibit two striking and ostensibly unrelated behaviours: in-context learning (ICL) and repetitive generation. In both, the model behaves as though it had summarised the context into a population-level statistic and discarded token-level detail. We ask whether this ``summarisation and forgetting'' can be derived from the attention mechanism itself, and answer in the affirmative. Under stationary, ergodic and elliptical inputs, the softmax attention output converges almost surely to $Θ_VΣΘ_K^{\top}Θ_Q x_t$, where $Σ$ is the input covariance; the long-context limit is therefore a linear readout of the input's second-order statistics. Two consequences follow. (i) For in-context linear regression, a single softmax head can implement one step of population gradient descent. Stacking such heads with residual connections iterates this update and implements multiple gradient descent steps. (ii) Propagated across an $L$-layer transformer, this readout drives the terminal hidden state at the parametric $1/t$ rate to a deterministic function of the current token alone, so that autoregressive generation collapses asymptotically to a first-order Markov chain whose attracting orbits furnish a structural account of repetition and mode collapse. The two phenomena thus emerge as facets of a single covariance-readout principle.

Speculative decoding speeds up autoregressive generation in Large Language Models (LLMs) through a two-step procedure, where a lightweight draft model proposes tokens which the target model then verifies in a single forward pass. Although the drafter network is small in modern architectures, its LM-head still performs projection to a large vocabulary, becoming one of the major computational bottlenecks. In prior work this issue has been predominantly addressed via static or dynamic vocabulary truncation. Yet mitigating the bottleneck, these methods bring in extra complexity, such as special vocabulary curation, sophisticated inference-time logic or modifications of the training setup. In this paper, we propose SlimSpec, a low-rank parameterization of the drafter's LM-head that compresses the inner representation rather than the output, preserving full vocabulary support. We evaluate our method with EAGLE-3 drafter across three target models and diverse benchmarks in both latency- and throughput-bound inference regimes. SlimSpec achieves $4\text{-}5\times$ acceleration over the standard LM-head architecture while maintaining a competitive acceptance length, surpassing existing methods by up to $8\text{-}9\%$ of the end-to-end speedup. Our method requires minimal adjustments of training and inference pipelines. Combined with the aforementioned speedup improvements, it makes SlimSpec a strong alternative across wide variety of draft LM-head architectures.

Diffusion large language models (dLLMs) offer a promising route to parallel and efficient text generation, but improving their reasoning ability requires effective post-training. Reinforcement learning with verifiable rewards (RLVR) is a natural choice for this purpose, yet its application to dLLMs is hindered by the absence of tractable sequence-level log-ratios, which are central to standard policy optimization. The lack of tractable sequence-level log-ratios forces existing methods to rely on high-variance ELBO-based approximations, where high verifier rewards can amplify inaccurate score estimates and destabilize RL training. To overcome this issue, we propose \textbf{R}elative \textbf{S}core \textbf{P}olicy \textbf{O}ptimization (RSPO), a simple RLVR method that uses verifiable rewards to calibrate noisy likelihood estimates in dLLMs. The core of our algorithm relies on a key observation: a reward advantage can be interpreted not only as an update direction, but also as a target for the relative log-ratio between the current and reference policies. Accordingly, RSPO calibrates this noisy relative log-ratio estimate by comparing its reward advantage with the reward-implied target relative log-ratio, updating the policy according to the gap between the current estimate and the target rather than the raw advantage alone. Experiments on mathematical reasoning and planning benchmarks show that RSPO yields especially strong gains on planning tasks and competitive mathematical-reasoning performance.

Generating high-fidelity synthetic GPS trajectories is increasingly important for applications in transportation, urban planning, and what-if scenario simulation, especially as privacy concerns limit access to real-world mobility data. Existing trajectory generation models face a trade-off between efficiency and faithfulness to road network topology: continuous-space methods enable fast generation but ignore the road network, while topology-aware approaches rely on search-based autoregressive decoding that limits generation speed. We propose TrajDLM, a topology-aware trajectory generation framework based on block diffusion language models that bridges this gap. TrajDLM models trajectories as sequences of discrete road segments, combining a block diffusion backbone for efficient denoising, topology-aware embeddings from a road network encoder, and topology-constrained sampling to ensure coherent and realistic trajectories. Across three city-scale datasets, TrajDLM achieves strong performance on fine-grained local similarity metrics while being up to $2.8\times$ faster than prior work, and demonstrates strong zero-shot transfer across domains, including unseen transportation modes. These results highlight the effectiveness of block-wise discrete diffusion as a scalable approach to accurate and efficient trajectory generation. Our code is available at https://github.com/cruiseresearchgroup/TrajDLM/

Generative models trained on finite data face a fundamental tension: their score-matching or next-token objective converges to the empirical training distribution rather than the population distribution we seek to learn. Using rule-valid synthetic tasks, we trace this tension across two training timescales: $τ_{\mathrm{rule}}$, the step at which generations first become rule-valid, and $τ_{\mathrm{mem}}$, the step at which models begin reproducing training samples. Focusing on parity and extending to other binary rules and combinatorial puzzles, we characterize how these two clocks, $τ_{\mathrm{rule}}$ and $τ_{\mathrm{mem}}$, depend on key aspects of the learning setup. Specifically, we show that $τ_{\mathrm{rule}}$ increases with rule complexity and decreases with model capacity, while $τ_{\mathrm{mem}}$ is approximately invariant to the rule and scales nearly linearly with dataset size $N$. We define the \emph{innovation window} as the interval $[τ_{\mathrm{rule}}, τ_{\mathrm{mem}}]$. This window widens with increasing $N$ and narrows with rule complexity, and may vanish entirely when $τ_{\mathrm{rule}} \geq τ_{\mathrm{mem}}$. The same two-clock structure arises in both diffusion (DiT) and autoregressive (GPT) models, with architecture-dependent offsets. Dissecting the learned score of DiT models reveals a corresponding evolution of the optimization landscapes, where rule-valid samples' basins expand substantially around $τ_{\mathrm{rule}}$, while training samples' basins begin to dominate around $τ_{\mathrm{mem}}$. Together, these results yield a unified and predictive account of when and how generative models exhibit genuine innovation.

Diffusion language models (DLMs) have recently emerged as a promising alternative to autoregressive models, primarily due to their ability to enable parallel decoding. Despite this advantage, most existing DLMs rely on a fixed generation length specified prior to decoding, which restricts their flexibility in real-world applications. While a few recent works attempt to support flexible-length generation, they typically suffer from notable limitations: some require costly retraining to accommodate variable-length outputs, while others depend solely on local confidence signals during decoding. Such local criteria fail to capture the evolving structure of the sequence, often resulting in suboptimal generation quality. In this paper, we propose a training-free, Bayesian structured decoding framework that formulates flexible-length generation as a dynamic structural inference problem. Our approach formulates flexible-length generation as a dynamic structural inference problem, jointly computing the expansion length, the block boundaries, and the decoding schedule. At each window expansion step, the method integrates local uncertainty with structural signals via a unified mechanism that supports dynamic structured generation, including both flexible block expansion and block organization, while maintaining coherence. Extensive experiments across multiple benchmarks demonstrate that our approach significantly improves generation quality and flexibility over existing fixed-length and flexible-length baselines. These results highlight the advantage of Bayesian structured decoding for diffusion language model, providing a principled and efficient solution for structured text generation.

Masked diffusion language models enable parallel token generation and offer improved decoding efficiency over autoregressive models. However, their performance degrades significantly when generating multiple tokens simultaneously, due to a mismatch between token-level training objectives and joint sequence consistency. In this paper, we propose ME-DLM, an edit-based refinement framework that augments diffusion generation with lightweight post-editing steps. After producing an initial complete response, the model refines it through minimal edit operations, including replacement, deletion, and insertion, conditioned on the full sequence. Training supervision is derived from edit distance, providing a deterministic signal under a fixed canonicalization scheme for learning minimal corrections. This approach encourages sequence-level consistency through globally conditioned edits while preserving the efficiency benefits of parallel diffusion decoding. Extensive experiments demonstrate that ME-DLM improves the quality and robustness of multi-token parallel generation. In particular, when built upon LLaDA, our method achieves consistent gains of 11.6 points on HumanEval and 33.6 points on GSM8K while using one-eighth of the total diffusion steps. Code is available at https://github.com/renhouxing/ME-DLM.

Diffusion large language models (dLLMs) offer a promising paradigm for parallel text generation, but in practice they face an accuracy-parallelism trade-off, where increasing tokens per forward (TPF) often degrades generation quality. Existing acceleration methods often gain speed at the cost of accuracy. To address this limitation, we propose TAD, a Temporal-Aware trajectory self-Distillation framework. During data construction, we condition a teacher model on both the prompt and the ground-truth response to generate decoding trajectories, recording the intermediate masked states throughout the process. Based on how many decoding steps remain before each masked token is revealed, we partition masked positions into near and distant subsets. For near tokens, we train the student with a hard cross-entropy loss using the teacher trajectory tokens as labels, encouraging confident predictions for tokens that are about to be decoded. For distant tokens, we apply a soft KL divergence loss between the teacher and student token distributions, providing softer supervision and preserving future planning knowledge. This temporal-aware partition naturally gives rise to two deployment configurations: a Quality model that prioritizes accuracy and a Speed model that favors more aggressive acceleration. Experiments show that TAD consistently improves the accuracy-parallelism trade-off. On LLaDA, it raises average accuracy from 46.2% to 51.6% with the Quality model and average AUP from 46.2 to 257.1 with the Speed model. Our code is available at: https://github.com/BHmingyang/TAD

Attention sinks -- tokens that receive disproportionate attention mass -- are assumed to be functionally important in autoregressive language models, but their role in diffusion transformers remains unclear. We present a causal analysis in text-to-image diffusion, dynamically identifying dominant attention recipients per timestep and suppressing them via paired, training-free interventions on the score and value paths. Across 553 GenEval prompts on Stable Diffusion~3 (with SDXL corroboration), removing these sinks does not degrade text-image alignment (CLIP-T) or preference proxies (ImageReward, HPS-v2) at $k{=}1$; only under stronger interventions ($k\!\geq\!10$) does HPS-v2 exhibit a metric-dependent boundary, while CLIP-T remains robust throughout. The perceptual shifts induced by suppression are nonetheless \emph{sink-specific} -- $\sim\!6\times$ larger than equal-budget random masking -- revealing an empirical dissociation between trajectory-level perturbation and \emph{semantic alignment} in diffusion transformers. \footnote{Code available at https://github.com/wfz666/ICML26-attention-sink.}

Diffusion language models (DLMs) offer a structural alternative to autoregressive generation: denoising can update tokens in arbitrary orders or in parallel rather than along a fixed left-to-right chain. In practice, fast DLM decoding remains strongly order-sensitive and often drifts toward autoregressive-like trajectories. We trace this tension to compatibility. At each reverse-time step, a DLM provides local denoising conditionals over the unresolved tokens. Arbitrary-order denoising becomes well defined when these local conditionals compose into order-invariant pseudo-joints. We formalize this view by defining order-induced pseudo-joints and a local denoising circulation: the log-ratio between the two pseudo-joints obtained by swapping a pair of unresolved positions. This circulation is zero under compatible conditionals, and global order gaps decompose into sums of local circulations along adjacent swaps. We further separate incompatibility-driven path dependence from conditional-dependence error in parallel updates and from order-specific estimation error. The resulting framework provides inference-only diagnostics for testing when DLM decoding is genuinely order-free.

Selecting a coherent sequence or subset of elements is a fundamental problem in structured prediction, arising in tasks such as detection, trajectory forecasting, and representative subset selection. In many such settings, the target is inherently ambiguous: each input admits multiple valid outputs, while supervision provides only a single sampled instance. This induces a mismatch between the underlying multi-modal target distribution and the observed training signal. We propose Contextual Plackett-Luce (CPL), a structured probabilistic model for sequence selection that extends the classical Plackett-Luce model to a context-dependent setting following an Ising-style parameterization with unary and pairwise interaction terms. CPL can be viewed as a hybrid between fully autoregressive prediction and parallel sequence selection: autoregressive models effectively capture uncertainty but are computationally expensive on modern parallel hardware such as GPUs, while parallel methods are efficient but struggle to represent multi-modal dependencies. CPL combines the strengths of both by constructing the parameters of a probabilistic selection model in a fully parallel manner, followed by a lightweight autoregressive selection process in which each step applies incremental updates to contextual logits. This decoupling of parallel scoring and sequential selection enables efficient computation without sacrificing expressivity. We evaluate CPL on two structured selection tasks: multi-modal path prediction and representative subset selection. CPL achieves improved structural consistency and robustness under ambiguous supervision compared to strong parallel baselines.

We investigate the geometry of predictive information across the layers of large language models (LLMs). We repurpose representation lenses-learned affine maps trained to predict the next token from intermediate residual streams-as geometric diagnostic tools. Rather than asking what the model predicts at each layer, we ask where predictive information resides and how it evolves across depth. We define at each layer a predictive readout subspace as the dominant k-dimensional singular subspace of such a map on the d-dimensional residual stream (where k is a resolution parameter), and track its trajectory on the Grassmann manifold as a similarity profile across layers. The profile is well described by unimodal distributions exhibiting a rise, near-plateau, and descent; varying k from 1% to 50% of d traces a Pareto frontier between visibility and energy retention, yet the same structure emerges at all scales. Across eight models from two families (Qwen2.5 and OLMo2, 1B-32B), we identify three geometric phases. Updates are approximately orthogonal to the residual stream throughout; what distinguishes the phases is their effect on the effective rank, which expands, stabilizes, and concentrates. In the first, Seeding Multiplexing, feed-forward memories and attention layers seed a candidate set in superposition in family-specific proportions, with the final token rising as leading candidate from 20% to 35% of positions across this phase. In the second, Hoisting Overriding, updates override existing subspaces to concentrate the candidate distribution without expanding the rank. In the third, Focal Convergence, high-energy low-rank updates write the winner into a form aligned with the unembedding direction. Phases 1 and 3 grow slowly with model depth, while Phase 2 expands linearly. The additional capacity of deeper LLMs is largely absorbed by candidate disambiguation.

We present TailedTS, a large-scale benchmark dataset derived from Wikipedia hourly page view observations throughout 2024, specifically designed to test time series forecasting models under heavy-tailed, zero-inflated, and non-Gaussian conditions. The dataset comprises approximately 24.69 billion data points spanning roughly 3 million unique Wikipedia pages per month, stored in high-efficiency Apache Parquet format. Wikipedia traffic follows a pronounced power-law distribution where roughly 5% of pages account for over 70% of total page views, creating a natural and rigorous testbed for model robustness against extreme volatility that are absent from or underrepresented in existing benchmarks such as M4, M5, and UCI electricity datasets. TailedTS enables several research tasks. First, we introduce a periodicity quantification framework based on sparse autoregression with sparsity and non-negativity constraints, revealing that frequently-viewed pages exhibit significantly weaker periodic structure than their less-viewed counterparts, showing direct implications for server allocation and traffic forecasting on large digital platforms. Second, we provide standardized prediction benchmarks evaluated under a suite of non-Gaussian loss functions, including $\ell_1$-norm, Huber, quantile, and $\ell_p$-norm losses, demonstrating that standard Gaussian-based estimators degrade substantially on high-volume page categories, while robust alternatives provide consistent gains across all traffic scales. TailedTS is publicly available at https://doi.org/10.5281/zenodo.17070469.

Autoregressive inference is typically assumed to scale predictably with decoding length, with latency increasing smoothly as generated sequence length grows. In this work, we identify unexpected non-monotonic latency behavior in the Apple MPS backend, where latency changes abruptly across nearby decoding configurations during transformer decoding. Using multiple model families (GPT-2, BLOOM, and OPT), we observe latency spikes of up to 21x within specific decoding-budget intervals, followed by recovery at neighboring configurations. Controlled experiments show that these anomalies originate primarily during the decode phase rather than prefill, are not explained by memory pressure alone, and remain absent on CPU and NVIDIA CUDA backends under identical conditions. We further show that key-value (KV) cache interacts strongly with these pathological execution regimes: KV caching remains beneficial overall, but its practical speedup collapses sharply within anomalous configurations, while cache-disabled decoding still exhibits residual non-monotonic behavior. These findings suggest that autoregressive decoding on MPS enters discrete execution regimes that are not captured by coarse-grained benchmarking, highlighting the importance of hardware-aware evaluation for long-context inference.

Autoregressive neural simulators now match classical solvers on short-horizon prediction of physical systems, yet their accuracy degrades rapidly when rolled out over long horizons. In this work, we identify transient amplification of perturbations around rollout trajectories as a structural mechanism driving rollout error. Using a linearization analysis we show that when the Jacobians along an autoregressive trajectory are non-normal and non-commuting, the model amplifies errors transiently, resulting in model rollout drift even when the overall system is asymptotically stable. Building on the analysis, we propose commutativity regularization: a combination of two penalties designed to reduce the normality defect of individual Jacobians and the commutator norm of Jacobians across steps. The penalties are estimated with Jacobian-vector products and have no inference-time cost. We show a propagator bound that quantifies rollout error under approximate commutativity and normality. We evaluate UNet and FNO variants with commutativity regularization on 1D and 2D spatio-temporal data in synthetic and real settings, showing successful long-horizon rollouts over thousands of steps. Further, we show that the method improves FourCastNet climate forecasts on ERA5 without using any new data. The gain is most pronounced out-of-distribution: trained on trajectories of a few hundred steps, regularized models remain in-distribution for thousands of rollout steps on initial conditions where baselines diverge.

Hair is a rich medium of visual and cultural expression, yet its digital modeling remains challenging due to the duality of fluidity and structure. Many existing generative approaches rely primarily on continuous diffusion fields, which entangle global topology with local texture and obscure the semantic and structural organization of hairstyles. To address this, we propose HairGPT, a strand-centric framework that treats strands as generative primitives and formulates realistic 3D hairstyle synthesis as a dual-decoupled autoregressive sequence modeling problem. Our method applies spatial decoupling across semantic scalp regions and structural decoupling along a hierarchical strand representation, progressing from global layout to fine-grained style. We further introduce a geometric tokenizer and region-aware semantic annotations to guide strand-level generation, enabling compositional editing, synthesis of rare and complex hairstyles, and adaptation to stylized domains. By aligning generative modeling with the workflow of digital grooming, HairGPT turns hair generation from opaque texture synthesis into a structured and semantically controllable authoring process, supporting robust semantic conditioning and high-fidelity results across realistic and stylized domains. Project Page: https://haiminluo.github.io/hairgpt/

Autoregressive (AR) models can generate high-quality low-poly meshes from point clouds, but they still operate in an all-or-nothing manner: when a local region is unsatisfactory, the entire mesh must be regenerated, wasting computation and destroying satisfactory mesh structure elsewhere. We introduce MeshFIM, a Fill-in-the-Middle (FIM) framework that regenerates a target region of a low-poly mesh conditioned on the surrounding context. MeshFIM addresses three mesh-specific challenges: enforcing exact attachment along the exposed boundary, preserving topological order in the context, and suppressing overflow beyond the intended region. It does so with five complementary design choices: boundary vertex markers, context positional embeddings, expanded context width, context augmentation, and a low-poly geometry encoder whose gated subtraction mechanism focuses generation on the missing region by leveraging the difference between the reference surface and the existing mesh. Detailed ablation studies are presented to show the effectiveness of every introduced component. Based on MeshFIM, we demonstrate two applications: interactive brush-based editing and automatic defect repair on low-poly mesh (see Figure 1). Last but not least, experiments show that MeshFIM outperforms a range of baselines in mesh refinement, mesh repair and whole mesh generation plus stitch-back scheme.

Diffusion Language Models (dLLMs) have garnered significant attention for their potential in highly parallel processing. The parallel capabilities of existing dLLMs stem from the assumption of conditional independence at high confidence levels, which ensures negligible discrepancy between the marginal and joint distributions. However, the stringent confidence thresholds required to preserve accuracy severely constrain the scalability of parallelism. Through systematic token-level statistical analysis, we reveal that a substantial proportion of tokens converge to their correct predictions early in the denoising process yet fail to reach standard confidence thresholds, confirming that current confidence-based criteria are overly conservative. In response, we introduce LEAP (Lookahead Early-Convergence Token Detection for Accelerated Parallel Decoding). LEAP is a training-free, plug-and-play method that leverages future context filtering and multi-sequence superposition to detect early-converging tokens. By validating the alignment between early convergence and correctness, we enable reliable early decoding of these tokens. Benchmarking across diverse domains demonstrates that LEAP significantly lowers inference latency and decoding steps. Compared to confidence-based decoding, the average number of denoising steps is reduced by about 30%. On the GSM8K dataset, combining LEAP with dParallel accelerates decoding to 7.2 tokens per step while preserving model precision. LEAP effectively breaks the reliance on high-confidence priors, offering a novel paradigm for parallel decoding.

Discrete diffusion language models (DLMs) generate text by iteratively denoising all positions in parallel, offering an alternative to autoregressive models. Controlled generation methods for DLMs, imported from autoregressive models, apply uniform intervention at every denoising steps. We show this uniform schedule degrades quality, and the damage compounds when multiple attributes are steered jointly. To diagnose the failure, we train sparse autoencoders on four DLMs (124M-8B parameters) and find that different attributes commit on distinct schedules, varying in timing, sharpness, and magnitude. For instance, topic commits within the first 2% of denoising, whereas sentiment emerges gradually over 20% of the process. Consequently, uniform intervention wastes steering capacity on steps where the target attribute has already solidified or has yet to emerge. We propose a novel adaptive scheduler that concentrates interventions on the steps where an attribute is actively forming and leaves the rest of generation untouched. The cost-control trade-off admits a closed-form characterization: the advantage of adaptive over uniform scheduling is governed by a single dispersion statistic of the commitment distribution. Across four DLMs and seven steering tasks, our method achieves precise control without the degradation typical of uniform interventions. Especially on challenging simultaneous three-attribute control, it reaches up to 93% steering strength, beating the strongest baseline by up to 15% points while preserving generation quality.

Recent byte-level language models (LMs) match the performance of token-level models without relying on subword vocabularies, yet their utility is limited by slow, byte-by-byte autoregressive generation. We address this bottleneck in the Byte Latent Transformer (BLT) through new training and generation techniques. First, we introduce BLT Diffusion (BLT-D), a new model and our fastest BLT variant, trained with an auxiliary block-wise diffusion objective alongside the standard next-byte prediction loss. This enables an inference procedure that generates multiple bytes in parallel per decoding step, substantially reducing the number of forward passes required to generate a sequence. Second, we propose two extensions inspired by speculative decoding that trade some of this speed for higher generation quality: BLT Self-speculation (BLT-S), in which BLT's local decoder continues generating past its normal patch boundaries to draft bytes, which are then verified with a single full-model forward pass; and BLT Diffusion+Verification (BLT-DV), which augments BLT-D with an autoregressive verification step after diffusion-based generation. All methods may achieve an estimated memory-bandwidth cost over 50% lower than BLT on generation tasks. Each approach offers its own unique advantages, together removing key barriers to the practical use of byte-level LMs.

Latent diffusion models offer an attractive alternative to discrete diffusion for non-autoregressive text generation by operating on continuous text representations and denoising entire sequences in parallel. The major challenge in latent diffusion modeling is constructing a suitable latent space. In this work, we present the Latent Diffusion Language Model (LDLM), in which the latent encoder, diffusion model, and decoder are trained jointly. LDLM builds its latent space by reshaping the representations of a pre-trained language model with a trainable encoder, yielding latents that are easy to both denoise and decode into tokens. We show that naive joint training produces a low-quality diffusion model, and propose a simple training recipe consisting of an MSE decoder loss, diffusion-to-encoder warmup, adaptive timestep sampling, and decoder-input noise. Ablations show that each component substantially impacts generation performance. On OpenWebText and LM1B, LDLM achieves better generation performance than existing discrete and continuous diffusion language models while being $2{\text -}13\times$ faster, indicating that jointly learning the latent space is a key step toward making latent diffusion competitive for text generation.

Discrete flow matching generates text by iteratively transforming noise tokens into coherent language, but may require hundreds of forward passes. Distillation uses the multi-step trajectory to train a student to reproduce the process in a few steps. When the student underperforms, the usual explanation is insufficient capacity. We argue the opposite: the trajectory is the bottleneck, not the student. Each training trajectory is built through a chain of blind stochastic jumps with no evaluation of sequence quality; a single bad decision at an early midpoint propagates through subsequent steps, yet the student must imitate the result. Trajectory-Shaped Discrete Flow Matching (TS-DFM) replaces these blind jumps with guided navigation: a lightweight energy compass evaluates candidate continuations at each midpoint, selecting the most coherent. All shaping is training-only; inference cost is unchanged. On 170M-parameter language modeling, the shaped student at 8 steps achieves 32% lower perplexity than the 1,024-step teacher while being 128x faster, with gains consistent across source distributions and three evaluators of increasing scale. TS-DFM achieves the best perplexity of any discrete-generation baseline we compare against, including methods trained on 6x more data or using 5x larger models.

Coarse-mask local image editing asks a model to modify a user-indicated region while preserving the surrounding scene. In practice, however, rough masks often become unintended shape priors: instead of serving as flexible edit support, the mask can pull the generated object toward its accidental boundary. We study this failure as mask-shape bias and frame the task through a Two-Zone Constraint, where the background should remain stable while the editable region should follow the instruction without being forced to inherit the mask contour. BRIDGE addresses this setting by keeping masks outside the DiT backbone for support construction and blending, avoiding DiT-internal mask injection and copied control branches. It uses BridgePath generation, where a Main Path preserves background context and a Subject Path generates editable content from independent noise. Motivated by a diagnostic Qwen-Image experiment showing that positional embeddings and attention connectivity regulate which image context visual tokens reuse, BRIDGE introduces a learnable Discrete Geometric Gate for token-level positional-embedding routing. This gate lets subject tokens borrow background-anchored coordinates near fusion regions or keep subject-centric coordinates for geometric freedom. We evaluate BRIDGE on BRIDGE-Bench, MagicBrush, and ICE-Bench. On BRIDGE-Bench, BRIDGE improves Local SigLIP2-T from 0.262 with FLUX.1-Fill and 0.390 with ACE++ to 0.503, with parallel gains in local DINO and DreamSim. Zero-shot results on MagicBrush and ICE-Bench further indicate competitive alignment and source preservation beyond the curated benchmark, while the added routing module remains compact at 13.31M parameters compared with ControlNet-style copied branches.

Continuous diffusion and flow matching models could represent a powerful alternative to autoregressive approaches for language modelling (LM), as they unlock a host of advantages currently reserved for continuous modalities, including accelerated sampling and tilting. Recently, several works have demonstrated the possibility of generating discrete data continuously by a simple flow matching process between a Gaussian and the one-hot encoded data distribution. They have further shown the feasibility of accelerated sampling via Categorical Flow Maps (CFMs), resulting in competitive sample quality in the few-step regime. However, this method had only been evaluated at relatively modest scales ($<1$B), leaving the question of its scalability completely open. In this article, we train a $1.7$B-parameter base flow model on $2.1$T tokens and self-distill it into a CFM that generates diverse, high-quality text in as few as $4$ inference steps while maintaining near-data-level token entropy. Furthermore, we introduce a likelihood bound for CFMs in the semi-discrete setting, and show that they can be used to score the model on standard LM benchmarks, achieving results in the same range as discrete diffusion methods. Finally, we uncover some of the challenges that arise from training these models at scale, and we provide prescriptive insights on loss weighting and time scheduling.

Diffusion Transformers (DiT) trained with flow matching in a VAE latent space have unified visual generation across images and videos. A natural next step toward a single architecture for both generation (visual synthesis) and understanding (text generation) is to apply this framework to language modeling. We propose TextLDM, which transfers the visual latent diffusion recipe to text generation with minimal architectural modification. A Transformer-based VAE maps discrete tokens to continuous latents, enhanced by Representation Alignment (REPA) with a frozen pretrained language model to produce representations effective for conditional denoising. A standard DiT then performs flow matching in this latent space, identical in architecture to its visual counterpart. The central challenge we address is obtaining high-quality continuous text representations: we find that reconstruction fidelity alone is insufficient, and that aligning latent features with a pretrained language model via REPA is critical for downstream generation quality. Trained from scratch on OpenWebText2, TextLDM substantially outperforms prior diffusion language models and matches GPT-2 under the same settings. Our results establish that the visual DiT recipe transfers effectively to language, taking a concrete step toward unified diffusion architectures for multimodal generation and understanding.