Diffusion Models

The diffusion based robot navigation world models are typically trained using parallel supervision, while autoregressive inference is employed during path planning. This results in a distribution shift between training and inference, which destabilizes the performance over long-horizon prediction. We propose AR Forcing, an autoregressive training strategy, which integrates the standard diffusion loss into the autoregressive training loop. At each step, the model uses its own predictions to update the context and optimize the single step noise prediction objective, thereby explicitly exposing the model to the inference state distribution during training. Our method does not require additional discriminators or distribution-matching losses, retains the original diffusion framework and sampler, and is easy to integrate. Experiments on multi-domain navigation datasets (RECON, SCAND, HuRoN, TartanDrive) show that compared with strong baselines, AR Forcing improved the consistency of generated images during long-horizon navigation and the accuracy of predicted trajectories, enhancing robustness of the model in complex known and unknown environments. We will release the code soon.

Therapeutic mRNA design requires coordinating multiple interacting sequence features across the full transcript, where codon usage, untranslated regions (UTRs), and their coupling jointly determine stability, translation efficiency, and protein expression. Here, we present mRNA generation via unrolled trajectories and informed latent updates (mRNAutilus), a framework for simultaneous codon optimization and de novo UTR design directly from sequence. mRNAutilus combines a masked discrete diffusion model trained on millions of full-length mRNAs with Monte Carlo Tree Guidance to generate Pareto-efficient sequences under multiple functional objectives, using lightweight regressors over model embeddings to predict half-life, translation efficiency, and protein abundance. Unlike recent methods that design coding sequences and UTRs separately or rely on post hoc assembly and screening, mRNAutilus generates complete transcripts in a single process optimized across properties. Across diverse targets, zero-shot mRNAs encoding P. pyralis luciferase achieve over 400-fold higher expression than wild-type and outperform commercial and machine learning-designed baselines, including zero-shot generative approaches. Zero-shot SARS-CoV-2 Spike mRNAs exceed clinically used and commercial constructs and match or surpass lab-optimized designs with improved durability. We further demonstrate generality in therapeutic settings, including prime editing (PEMax) and programmable proteome modulation, where mRNAutilus-designed constructs enhance expression of peptide-guided E3 ligases (uAbs) for beta-catenin degradation. These results establish a sequence-based, multi-objective framework for generating functional mRNAs tailored to diverse biological applications.

Riemannian diffusion models generalize score-based generative modeling to manifold-supported data via stochastic diffusion equations on the manifold. However, training requires sampling from and differentiating the manifold heat kernel, which is rarely available in closed form beyond a few highly symmetric manifolds. We propose a general approach that approximates the heat kernel by directly solving the manifold heat equation with a physics-informed neural network (PINN). Given an explicit manifold specification, we choose a coordinate system, derive the corresponding heat (Fokker--Planck) equation and a short-time asymptotic approximation, and then train a PINN to learn the log heat kernel. The resulting surrogate enables both forward noising (heat-kernel sampling) and conditional-score evaluation for denoising score matching. We demonstrate the method on diverse manifolds including $S^2$, $SO(3)$, $\mathrm{SPD}(n)$, and permutation-quotiented point clouds.

Real-time and accurate spatial audio generation is pivotal for delivering an immersive experience. However, existing spatial audio synthesis technologies are often encumbered by a tradeoff between generation quality and high inference latency, as well as difficulty in capturing precise spatial information from multimodal inputs. To address these challenges, we propose SwanSphere, a unified streaming framework for high-fidelity spatial audio generation from panoramic videos and text prompts. SwanSphere mainly makes the following contributions: 1) We introduce a causal autoregressive diffusion transformer architecture that enables streaming high-quality spatial audio generation. 2) We design a Spatial Video-Audio Contrastive (SVAC) learning strategy to align the video encoder with the acoustic domain, and further employ a multi-objective online direct preference optimization (ODPO) scheme, resulting in strong spatial perception and robust multimodal spatial audio synthesis. 3) To alleviate the current scarcity of spatial audio datasets, we also develop an automated annotation pipeline for generating detailed spatial captions. Experimental results demonstrate that SwanSphere achieves superior performance in both video-to-spatial and text-to-spatial audio generation tasks. Demos can be found at: https://swanaigc.github.io.

Diffusion-based neural solvers have shown strong promise for combinatorial optimization (CO), but existing methods typically rely on supervised training with large collections of near-optimal solutions. In this work, we extend adjoint-based trajectory optimization methods to discrete combinatorial domains. We formulate diffusion-based CO as a stochastic control problem over Continuous-Time Markov Chains and introduce discrete adjoint dynamics for propagating optimization signals through discrete generative trajectories. Building on this formulation, we propose Combinatorial Adjoint Matching (CAM), an unsupervised training framework for discrete diffusion solvers with structured and low-variance trajectory-level optimization signals. Empirically, CAM consistently outperforms existing unsupervised diffusion baselines and achieves performance competitive with strong supervised diffusion solvers and even traditional solvers across diverse combinatorial optimization problems. Our code is available at https://github.com/Shengyu-Feng/CAM.

Unlearning in diffusion models aims to remove undesirable data or concepts while preserving the utility of pretrained models -- two fundamentally conflicting objectives. We propose a principled constrained optimization framework that formulates unlearning as minimizing the deviation from a pretrained model, subject to explicit separation constraints from the unlearning distributions. Specifically, we formulate three constrained optimization problems based on reverse and forward KL divergences, and likelihood constraints. The first two generalize existing approaches for concept and data unlearning, while the third offers a novel and natural formulation for unlearning. Despite the nonconvexity of the KL constraints, we establish strong duality for all three problems, enabling us to explicitly characterize their optimal solutions as unlearning targets and develop primal-dual algorithms for each formulation. Experimental results demonstrate that our KL-constrained approach achieves superior retention-unlearning tradeoffs compared to weight-based baselines for concept and data unlearning, and that our likelihood-based approach matches unlearning effectiveness while better preserving retained concepts compared to baselines.

Generative models have a persistent limitation: their tendency to memorize training data can create legal liabilities and erode creative diversity. Understanding which samples are memorized in whole or in part, and under what conditions, therefore remains an important open problem. Here we answer the question "Are atypical or rare samples memorized first?" in the negative. We train diffusion models on strings generated according to the production rules of the Random Hierarchy Model (RHM), and find that samples composed of common substrings are preferentially memorized. This holds true even if the training data consists of entirely unique samples, indicating that deduplication at the data point level does not provide a meaningful privacy guarantee. Correspondingly we predict, then observe, delayed memorization for fat-tailed datasets (i.e., those with more atypical samples). This effect is amplified when fat-tails are introduced into high-level production rules. These together suggest that dataset diversity, particularly at higher levels of abstraction, plays an important role in staving off memorization. Finally, we identify an intermediate regime of partial memorization in which common substrings are learned first and subsequently overproduced during generation. If training is stopped in this regime, models will exhibit the reversion-to-the-mean blandness often derided as "slop".

I present diffusion models as part of a family of machine learning techniques that withhold information from a model's input and train it to guess the withheld information. I argue that diffusion's destroying approach to withholding is more flexible than typical hand-crafted information withholding techniques, providing a rich training playground that could be advantageous in some settings, notably data-scarce ones. I then address subtle issues that may arise when porting reinforcement learning techniques to the diffusion context, and wonder how such exploration problems could be addressed in more diffusion-native ways. I do not have definitive answers, but I do point my fingers in directions I deem interesting. A tutorial follows this thesis, expanding on the destroy-then-generate perspective. A novel kind of probabilistic graphical models is introduced to facilitate the tutorial's exposition.

With the rapid advancement of diffusion models, talking face generation has made remarkable progress. However, existing diffusion-based methods still require task-specific fine-tuning and large-scale audiovisual datasets, resulting in high computational costs that hinder scalability and accessibility of diffusion-based approaches across the research community. To address this, we propose a finetuning-free paradigm that directly performs talking face generation using the pretrained weights of Stable Diffusion and IP-Adapter. This backbone leverages the visual embedding capability of IP-Adapter to mine lip-related semantics from the pretrained Stable Diffusion. To address the challenges of identity drift, synchronization errors, and temporal instability, we also design three trainable-parameterfree components: (1) the Structurist, which explicitly disentangles and reassembles lip and appearance features to mitigate identity drift and appearance distortion; (2) the Structure Controller, which adaptively refines embeddings based on quasi-monotonic motion trends for precise lip synchronization; and (3) the Noise Sensor, which introduces Gaussian prior to detect and suppress flicker and jitter artifacts and enhance temporal consistency. Experimental results show that our method outperforms existing SOTA approaches in both lip-sync accuracy (at least 0.16 gain in PCLD) and visual fidelity (at least 0.7 improvement in FID), establishing a novel fine-tuning-free diffusion framework for talking face generation.

Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their statistical efficiency remains limited. Existing theories typically rely on strong regularity assumptions, such as uniformly bounded densities or globally smooth score functions, which fail to capture such intrinsic structures. In this work, we study the sample complexity of diffusion models for learning distributions supported on a union of low-dimensional subspaces. Assuming that the data distribution within each subspace is subgaussian, we show that diffusion models require at most $\widetilde{O}(\varepsilon^{-k \vee 2})$ samples to achieve $\varepsilon$ error in 1-Wasserstein distance, where $k$ is the intrinsic dimension. This near-optimal convergence rate depends only on the intrinsic dimension and significantly improves upon prior theoretical guarantees that suffer from the curse of dimensionality. Notably, our analysis applies to a broad collection of distributions without imposing smoothness, bounded-density, or log-concavity assumptions. Overall, our results show that diffusion models can statistically adapt to intrinsic low-dimensional structure while naturally accommodating multi-modal data, offering a rigorous theoretical justification for their success in complex high-dimensional learning tasks.

Anomaly detection aims to identify samples that deviate from the nominal data distribution and is central to many safety-critical applications. However, developing effective anomaly detection methods for categorical, mixed-type, and discrete sequence data remains challenging and relatively underexplored. Masked diffusion models provide a natural way to model such data by learning to recover masked values from the remaining visible context. In this paper, we propose Masked Diffusion for Anomaly Detection (MaskDiff-AD), a forward-only method based on masked diffusion models trained only on nominal data. Given a test sample, MaskDiff-AD constructs anomaly scores from the difficulty of reconstructing randomly masked coordinates, yielding a content-sensitive score that operates directly on discrete state spaces while avoiding reverse-time sampling. We also develop a non-parametric variant of MaskDiff-AD and provide theoretical guarantees by characterizing Type-I and Type-II errors under a fixed detection threshold. Experiments on fourteen categorical and mixed-type tabular datasets from ADBench and UADAD, as well as four text anomaly detection datasets from NLP-ADBench, show that MaskDiff-AD achieves competitive performance against classical, diffusion-based, and recent tabular/text anomaly detection baselines. Notably, MaskDiff-AD achieves the best overall average rank, outperforming all twelve tabular baseline methods.

Large-scale text-to-image (T2I) diffusion models have enabled unprecedented creative applications, but their unauthorized use has raised serious intellectual property concerns, making model ownership verification (MOV) increasingly critical. We find that existing backdoor-based diffusion watermarking methods often (implicitly) assume a "faithful" verification process, namely, that the verifier can query a suspicious model and obtain the faithful watermark response to complete MOV. However, in practice, adversaries may intentionally or unintentionally damage potential watermark signals, significantly degrading verification reliability. To address this issue, we propose Cert-LAS, the first certified MOV method for T2I models based on layer-adaptive smoothing. In general, Cert-LAS embeds specified watermarks using diffusion classifiers and an LFS-guided layer-adaptive noise, and verifies ownership by examining whether the suspected model exhibits significantly stronger watermark responses compared to unwatermarked references through hypothesis testing. We further prove that, under certain conditions, our Cert-LAS can still achieve reliable verification even in the presence of malicious removal attacks. Extensive experiments validate the effectiveness of Cert-LAS and its resistance to adaptive attacks. Our code is available at https://github.com/Leyi-Qi/Cert-LAS.

Collaborative driving systems leverage vehicle-to-everything (V2X) communication for multi-agent collaborative perception to enhance driving safety, yet they remain constrained by scarce annotated real-world V2X driving datasets and limited generalization across diverse driving conditions. While image generation technology offers a feasible solution for data augmentation, existing methods tailored for single-vehicle multi-view scenarios face two fundamental challenges in multi-agent driving settings: (1) the expansion of the learning objective degrades generation quality, and (2) the highly dynamic variations across agents hinder the modeling of consistency for physical attributes (e.g., color, category) in jointly observed objects. To bridge this gap, we propose V2XCrafter, the first framework for generating controllable and realistic collaborative driving scene across agents' camera views. For effective learning, we develop a progressive multi-agent diffusion model based on a single-agent backbone, using neighboring agents' latent states as reference signals to progressively guide the single-to-multi diffusion. To address cross-vehicle inconsistency, we propose a cross-agent attention module that leverages a collaboration view graph and learnable jointly observed object representation to model the dynamic cross-agent camera view relationships. Experiments have shown that V2XCrafter can generate high-fidelity and controllable street views with consistency across agents, thereby effectively enhancing the downstream collaborative 3D object detection tasks.

Diffusion bridge models offer a powerful framework for connecting two data distributions, such as in image restoration and translation. Many existing methods learn this bridge by mimicking the score-matching formulation of standard diffusion models. In this work, we find that this way leads to an anomalous underfitting phenomenon near the target endpoint, as the process approaches the target distribution ($t \to 0$). This underfitting, characterized by significant drift in the predicted variance and direction, results from an excessively large discrepancy in noise levels between the network's input and its regression target.To resolve this issue, we propose the Noise-Aligned Diffusion Bridge (NADB).Our approach reformulates the diffusion bridge by first employing a mean network to provide a cleaner conditional target, and then introducing a novel, noise-aligned mapping relationship. This new formulation resolves the noise mismatch and corrects the underfitting near the target endpoint. Experimental validation across multiple image restoration and image translation tasks demonstrates the effectiveness of our approach. Code is available at https://github.com/gyr02/NADB.

Concept erasure has emerged as a promising approach to mitigate undesired or unsafe content in diffusion models, yet existing methods still face significant limitations. While training-based methods are effective, their high computational cost limits scalability. Editing-based methods are more efficient and deployment-friendly, yet they struggle to simultaneously achieve precise concept erasure and preserve overall generative capacity. We identify this core limitation of the editing-based methods as reliance on additive parameter updates. Our empirical analysis reveals that concept semantics primarily depend on neuron direction rather than neuron magnitude, while overall generative capacity relies on the angular geometry of neurons. As additive updates inherently entangle direction, magnitude, and angular geometry, they inevitably introduce unintended interference between concept erasure and overall generation performance. To address this, we propose Orthogonal Concept Erasure (OCE), which reformulates editing-based erasure as multiplicative parameter updates from a geometric perspective. Specifically, OCE applies layer-wise orthogonal transformations derived from a closed-form solution to the parameters, enabling precise concept erasure while preserving the neuron magnitude and angular geometry. Furthermore, to address conflicting constraints in multi-concept erasure, OCE introduces a subspace-level objective with structured subspace manipulation, yielding a more effective and scalable erasure. Extensive experiments on single- and multi-concept erasure demonstrate that OCE outperforms existing methods in concept erasure and non-target preservation, erasing up to 100 concepts in 4.3 s. Code: https://github.com/HansSunY/OCE.

We present DEMON, a real-time diffusion engine that makes the denoising process playable as a live musical instrument: a control surface both broad (many parameters shaped per-frame across the output) and responsive (each control taking effect as fast as its place in the denoising loop allows). Built on ACE-Step 1.5 and StreamDiffusion's ring-buffer architecture with TensorRT acceleration, it sustains up to 12.3 decoder completions per second for 60-second music on a single consumer GPU (RTX 5090), or 11.3 generations per second at our production ring-depth of 4. At these rates denoising parameters become viable as live performance controls, but the ring buffer propagates per-request changes only at its drain rate, a floor of S denoising steps. We contribute four mechanisms. (1) Per-slot heterogeneous denoise scheduling: each ring-buffer slot owns its timestep schedule, so a moving denoise slider is tracked without wiping the in-flight queue, where the upstream global-schedule design must rebuild and discard it. (2) Shared mutable per-step state, giving any parameter consulted at every solver step next-tick effect, bypassing ring-buffer drain. (3) Per-frame source blending: a sampling-time control on the standard SDE re-noise step, giving a framewise transformation-strength axis that complements scalar denoise scheduling. (4) Windowed VAE decode exploiting receptive-field analysis for an 8.0x decode speedup. Together these separate streaming-diffusion parameters into four propagation classes, by onset and convergence latency.

We introduce Spectral Guidance, a framework for controlling diffusion models by leveraging the intrinsic geometry of the generative process. As data is progressively corrupted by noise, only a small number of features remain informative for control. We characterize them as the singular functions of a conditional expectation operator and show that they can be learned via a self-supervised objective. Once recovered, this basis enables the projection of arbitrary guidance signals, such as labels, CLIP embeddings, or masks, directly onto the sampling trajectory. This approach allows for stable, high-fidelity control without retraining or denoiser backpropagation during sampling. Empirically, we improve conditional accuracy on CIFAR-10 by 37 percentage points over the strongest training-free baseline while offering $4\times$ faster sampling. Moreover, the same representations that support label and CLIP guidance also enable spatial control, such as mask-based guidance, without auxiliary models. Finally, our framework reveals a phase transition in the generative process, pinpointing the optimal time window for effective guidance.

Diffusion models have emerged as powerful generative approaches for missing-data imputation, yet most existing methods operate directly in data space and degrade when training data are heavily incomplete. We investigate whether shifting diffusion to a learned latent representation improves robustness under missing-completely-at-random (MCAR) corruption. To this end, we propose a two-stage framework: a robust VAE-based imputer first learns compact semantic features from incomplete observations, and a diffusion model is then trained in the resulting latent space. Across training missing rates, we perform a controlled comparison against pixel-space diffusion models under the same incomplete-data setting. The latent diffusion model maintains high sample quality and remains stable up to 50% missingness, while pixel-space diffusion degrades progressively as missingness increases. For downstream imputation, latent diffusion also achieves consistently better performance than pixel-space diffusion. These findings indicate that latent-space modeling mitigates artifact amplification from zero-imputed inputs and provides a more robust generative prior for incomplete-data learning. Overall, our results support latent diffusion as a strong and practically useful alternative to pixel-space diffusion for missing-data problems.

The boundary between real and diffusion-generated time series is becoming increasingly difficult to draw, yet detection in this domain remains underexplored, especially when the generator is unknown. We compare white-box detection, which requires access to the generator, against black-box detection, which operates on the raw signal alone. The white-box approach, a reconstruction-based detector adapted from the image domain, works well in in-distribution but breaks down under generator shift: reconstruction-based detection in images succeeds because large generic generators provide a near-universal reconstruction prior, and no analogous generator exists for time series. In contrast, a simple off-the-shelf classifier used as a black-box detector performs remarkably well, achieving an average F1 of 79.2, a 22.1% relative improvement over the white-box approach, and a TPR@1%FPR of 57.2. Diffusion-generated time series detection is therefore not a direct transfer of the image domain problem. This work provides the first systematic exploration of white-box and black-box detection for diffusion-generated time series. We close by identifying several open and promising directions.

The remarkable generation quality of modern diffusion models often comes at the cost of massive parameter counts, which necessitate server-side inference with significant computational costs and potential privacy risks. Consequently, there is growing momentum toward developing efficient on-device alternatives. While recent efforts have optimized text-to-image models for mobile hardware, they remain relatively bulky, typically ranging from 0.5B to 1B parameters. We present BlazeEdit, a highly efficient, generalist image-to-image diffusion model tailored for on-device deployment. By identifying that many practical image editing tasks do not require text-based guidance, we eliminate the text-conditioning components and develop a multi-task architecture that consolidates object removal, outpainting, tone correction, relighting, and sticker generation into a single, compact model of only 195M parameters. BlazeEdit achieves a substantial reduction in download size and memory overhead while maintaining competitive generation quality. It completes a full inference pass in just 290ms on a Pixel 10, delivering a seamless, privacy-preserving, and lightning-fast experience for generalist image editing on the edge.

Generative models, including diffusion models, are increasingly used as foundation models and adapted through sequential fine-tuning, making continual learning an essential problem setting. However, continual learning in such generative models remains poorly understood: after a task change, what aspects of the learned distribution are most easily lost, and what replay samples should be prioritized? We address these questions through the modern Hopfield energy. Recent links between modern Hopfield networks (MHNs) and diffusion models allow analyses in MHNs to be transferred to diffusion models. We introduce intrinsic forgetting as an increase in Hopfield energy after the task change. In tractable settings in an MHN, we prove that high-energy, outlier-like samples undergo a larger energy increase than cluster-like samples, implying that samples located in sharp, isolated basins are more forgettable. We further analyze memory replay and show that replay is particularly effective for high-energy samples, enabling an energy-based selection of replay samples. We validate these predictions in experiments on MHNs and two diffusion models under continual-learning settings: Stable Diffusion and a pixel-space DDPM. In these diffusion models, Hopfield energy tracks reconstruction-based forgetting, and replay experiments reveal energy-dependent mitigation of forgetting that is consistent with the MHN analysis.

Text-to-image diffusion models generate images by iterative denoising, so their internal layers produce trajectories of activations rather than single static representations. Sparse autoencoders (SAEs) have recently been used to decompose diffusion activations into interpretable features, but most approaches analyze individual timesteps or condition on time rather than learning from full trajectories. Training one SAE on whole trajectories would make each feature a single trajectory across timesteps, but adjacent activations are largely linearly predictable from one another, so such an SAE spends its latents on content carried forward from step to step. We introduce residualized temporal SAEs (ReSAE), which fit linear predictors between neighboring timesteps and represent each trajectory by its initial activation and the residuals these dynamics leave unexplained. Training an SAE on this representation is equivalent to training it on raw trajectories under a metric induced by the linear dynamics, and it encourages latents to capture structure beyond what is linearly predictable. Each latent's decoder direction maps back to activation space as a feature trajectory over denoising time. Across Stable Diffusion~1.5 and a Diffusion Transformer, ReSAE features span the whole trajectory while pinpointing when changes enter it, making ReSAE a natural tool for studying how a diffusion model generates an image over time.

Flow and diffusion generative models have established themselves as widely adopted density estimators for simulation-based inference (SBI), extending naturally from neural posterior estimation to likelihood and joint density estimation. Their principled optimization objectives and freedom from architectural constraints have driven rapid adoption across the natural sciences. Yet the most widely used SBI libraries remain PyTorch-based, leaving researchers who develop their forward models and analysis pipelines in JAX without a native option. We present GenSBI, an open-source library that implements flow matching, score matching, and denoising diffusion entirely in JAX. The library offers three transformer-based architectures - SimFormer, Flux1, and a novel Flux1Joint that extends gate-modulated transformer blocks to joint density estimation - all interchangeable through a unified interface that decouples generative method, neural backbone, and inference mode. GenSBI provides an end-to-end workflow from training through posterior calibration (SBC, TARP, LC2ST) and supports custom architectures with domain-specific embedding networks. We validate the framework on standard SBI benchmarks, achieving near-ideal mean C2ST scores (0.50-0.56, where 0.50 is ideal) on SBIBM tasks with minimal per-task tuning and well-calibrated posterior coverage across all tested configurations. The code is publicly available at https://github.com/aurelio-amerio/GenSBI.

Discrete diffusion models have achieved strong empirical performance in text and other symbolic domains, but, especially for uniform-rate models, they often require many steps to generate a single sample. Existing acceleration methods either rely on training additional quantities or suffer from slow mixing. In this work, we propose a novel Gibbs-based corrector for discrete diffusion models, termed Gibbs-Accelerated Discrete Diffusion (GADD). GADD leverages the structure of the concrete score function to construct Gibbs posterior likelihoods directly, without requiring any additional training beyond standard score estimation. We show that GADD achieves an overall sampling complexity of $\mathcal{O}(\mathrm{polylog} (\varepsilon^{-1}))$, yielding the first such rate for diffusion-based samplers for uniform-rate discrete diffusion models. We also conduct numerical experiments demonstrating the practical advantages of GADD across synthetic data, zero-shot text sampling, and zero-shot conditional music generation. These results corroborate the theory and show that GADD consistently improves sample quality and wall-clock efficiency over standard baselines, including vanilla Euler methods and CTMC correctors. Beyond this, our theoretical analysis introduces a novel framework for analyzing predictor-corrector methods in discrete diffusion models, which may be of independent interest. Unlike existing approaches that rely on the Girsanov change-of-measure technique, our method is based on an induction argument that tracks error propagation across predictor iterations while accounting for inaccuracies in the corrector updates.

Video Diffusion Transformers (DiTs) generate high-quality videos but demand substantial compute due to wide blocks, deep architectures, and iterative sampling. Recent methods reduce cost by compressing width, depth, or sampling steps, but typically commit to a fixed architecture that cannot adapt to individual inputs or denoising stages. We propose PARE (Pruning and Adaptive Routing for Efficient video generation), which jointly compresses width and depth with structure-aware pruning and input-adaptive routing. For width, we observe that attention heads specialize into spatial and temporal roles, and design importance scoring that accounts for this distinction to prevent motion-critical temporal heads from being pruned prematurely. For depth, we train a lightweight router conditioned on denoising timestep and visual content to dynamically select which blocks to execute at each step, enabling per-input compute adaptation rather than static block removal. A progressive pipeline first recovers width-pruned quality via distillation, then jointly optimizes the student and router to decouple the two learning objectives. Experiments on Wan2.1-14B for both image-to-video and text-to-video generation show that PARE substantially reduces per-step computation while preserving quality across VBench dimensions, and composes with step distillation for further acceleration.

The rapid advancement of diffusion-based image generation models has raised serious concerns regarding potential copyright and privacy infringements involving human-created data. Membership inference attacks (MIAs) have emerged as a promising tool for identifying unauthorized data usage during model training. Existing methods typically assess the ability of model to denoise perturbed suspect images as an indicator of membership status. However, the discriminative power of such features is highly dependent on the degree of model memorization and deteriorates significantly when applied to less exposed data (e.g., pre-training data). Although several methods attempt to enhance detection by leveraging internal model features, these features are generally inaccessible in mainstream closed-source image generation platforms, limiting their practicality. In this paper, we demonstrate that analyzing how a black-box diffusion model denoises a target image and corresponding perturbed textual instructions can reveal more distinctive membership cues. Based on this insight, we propose a black-box membership inference attack framework (named SD-MIA) that leverages a cross-modal data perturbation mechanism to detect pre-training data in diffusion models. We conduct extensive experiments on both a public benchmark dataset and a newly constructed dataset, each comprising pre-training membership and non-membership samples with identical distributions. Experimental results demonstrate that SD-MIA achieves superior performance compared to existing baselines, including those with the unfair advantage of accessing internal model features.

Sampling from learned high-dimensional distributions is a foundational computational problem. We introduce U-turn chains: Markov chains obtained by iterating short forward-backward steps of a diffusion model, in which each step proposes a move that remains on the learned data manifold and, paired with a Metropolis-Hastings correction, samples from energy-modified targets. For synthetic languages, we show that minimal U-turn dynamics undergoes an ergodicity-breaking phase transition driven by fragmentation of the data manifold; ergodicity is restored at larger U-turn magnitude. In the non-ergodic regime, low-level features relax faster than high-level ones, an ordering that inverts only at sufficiently large U-turn magnitude. We test these predictions on natural language and natural images. In both modalities, minimal U-turns relax slowly, especially for high-level features approximated by deep representations in CNNs or LLMs. The layer-ordering inversion appears only at large noise when mixing is efficient -- signatures consistent with strongly constrained, weakly mixing local dynamics. We discuss the implications of these results for sampling with diffusion models.

We characterize the pre-softmax attention matrix $\mathbf{QK^\top}$ in transformers as an associative memory matrix encoding pairwise associations between input features. By decomposing this matrix into its symmetric and skew-symmetric parts, we interpret the symmetric component as governing the structure of the energy landscape, and the skew-symmetric component as driving circulation on that landscape. Leveraging the energy formulation induced by the symmetric component, we derive Hopfield-style stability measures that quantify the stability of retrieved features. We observe meaningful correlations between Hopfield-style stability measures and the fidelity-diversity trade-offs in generation. Finally, we propose a controllable knob to modulate this trade-off by modifying the circulation of the underlying dynamics. Code is available at our GitHub (https://github.com/hyeon-cho/Attention-Symmetric-Decomposition).

Learning an energy-based model from data samples is a central problem in machine learning. Many recent and popular methods, such as denoising score matching for training energy-based diffusion models, use stochastic interpolants to corrupt data samples at different noise levels indexed by a time variable. This defines a joint density over both the data space and time, and most methods learn its energy through either spatial or temporal differences. We identify distinct failure modes for both of these approaches. To solve them, we propose Spatiotemporal Noise-Contrastive Estimation (stNCE), a framework for learning the energy through joint spatiotemporal differences. stNCE unifies many existing methods and leads to new training objectives. Experiments on images and molecules demonstrate performance competitive with state-of-the-art density estimation methods.

Diffusion models can unintentionally memorize training samples, raising concerns about privacy and copyright. While recent methods can detect memorization, they often rely on global or model-specific signals and provide limited insight into where memorization appears within a generated image. We provide a geometric characterization of local memorization as a coordinate-wise variance collapse. However, such collapse can also arise from intrinsic data constraints rather than overfitting. To isolate overfitting-driven memorization, we propose curvature-difference methods that subtract the curvature of an underfitted baseline, either the unconditional model or a less-trained version of itself. We further derive a score-difference proxy that provides a geometric explanation for the widely used score-difference-based detection metric. Experiments on Stable Diffusion, evaluated against ground-truth memorization masks, show that our method outperforms the prior attention-based localization method. Code is available at https://github.com/Gwangho99/mem-curv-diff.