Denoising Trajectory

We present GeomVLA, a Vision-Language-Action (VLA) model that unifies perception, latent scene motion prediction, and action generation within a shared robot-centric 3D coordinate frame. Our approach lifts pretrained VLM features into spatially grounded 3D scene tokens using depth and camera calibration, while retaining the semantic representations learned during VLM pretraining. We further introduce a 3D Scene Trajectory Denoiser, a task-conditioned module that learns a latent representation of how scene points are expected to move in 3D. Rather than executing the predicted trajectory as an open-loop plan, GeomVLA extracts intermediate motion tokens from the trajectory denoiser and uses them to condition a 3D flow-based action denoiser through geometry-aware attention. GeomVLA achieves state-of-the-art performance on CALVIN, competitive performance on LIBERO and RoboTwin2.0, and outperforms strong baselines in real-world manipulation settings without robot-action pretraining. Extensive ablations show that future-motion reasoning alone is insufficient: the primary gains are associated with maintaining geometric consistency among scene representation, motion prediction, and robot actions throughout the perception-to-action pipeline.

Although text-to-image diffusion models generally exhibit strong prompt-following ability, we identify a persistent and previously underexplored failure pattern in which a small subset of prompts differing only in the object consistently fails to realize the same target concept under identical generation settings. We term this phenomenon object-dependent concept brittleness. Such cases suggest systematic internal blind spots rather than random sampling noise. In this paper, we present an interpretability-oriented framework to audit and minimally correct these failures. Our key idea is to analyze denoising trajectories in a step-wise sparse autoencoder (SAE) space, where abstract style and attribute concepts become more separable than in the raw denoising representation. This sparse space enables us to compare successful and failed generations, identify concept dimensions whose evidence is missing, weakened, or temporally delayed, and construct class-level concept prototypes from reliable class-consistent samples. Based on this audit process, we introduce a lightweight inference-time correction strategy that interpolates denoising features toward the corresponding prototype in SAE space. Rather than serving as a task-specific retraining method, this intervention acts as a validation of the diagnosed concept deficiency. We evaluate the proposed framework on style and attribute failure cases across multiple diffusion backbones, with significant improvements in concept consistency, text fidelity, and repair success. Further analyses show that deeper denoising representations provide clearer concept structure, while early-stage intervention offers the strongest correction leverage. Code is available at https://github.com/Metecade/Object-Dependent-Concept-Brittleness.

We present FlashRender, a few-step generative rendering framework that retakes a source video along a target camera trajectory in seconds. We identify sampling-step-dependent camera control as a prominent manifestation of discretization error in existing multi-step generative rendering models and show that resolving this inconsistency substantially lowers denoising trajectory curvature, facilitating subsequent step distillation. To this end, we introduce Representation Transformation and Alignment (RETA), which aligns hidden source-video representations with target-video features from a frozen visual geometry model. This directly encodes the geometric transformation within the source-video stream, enabling sampling-step-consistent camera control. We then fine-tune the model with the MeanFlow objective on the lower-curvature denoising trajectory induced by RETA, allowing the model to more effectively address discretization error. Finally, we apply on-policy flow map distillation to correct self-rollout errors under fixed few-step sampling. Extensive experiments show that RETA, MeanFlow, and on-policy flow map distillation play complementary roles in few-step generative rendering. Together, they enable our approach to match multi-step baselines in video quality and geometric consistency at 25x lower sampling cost while achieving superior camera controllability, even under out-of-distribution target camera trajectories.

Diffusion models have achieved dominant performance in visual generation but suffer from substantial inference overhead. While cache-based acceleration has emerged as a promising solution, existing policies rely on local similarity heuristics, which we identify as being significantly misaligned with final generation quality. This discrepancy stems from the non-uniform propagation and accumulation of errors along the denoising trajectory. To address this, we propose Global-Impact Cache (GCache). We first establish a rigorous theoretical characterization of the error propagation upper bound. Recognizing that this bound can be overly conservative for complex, highly non-convex diffusion models, we further reparameterize the propagation exponent with a Bernstein form and reformulate cache policy search as a bilevel optimization problem. In detail, GCache identifies an optimal reuse policy in the inner objective while aligning the error-weighting function with generation quality loss in the outer objective. This framework effectively reconciles theoretical rigor with empirical performance, learning to prioritize computation where it most impacts visual fidelity. Extensive experiments demonstrate that GCache consistently outperforms prior caching strategies on both video and image generation. Notably, on the state-of-the-art Wan2.1 video diffusion model, GCache maintains a 2.17x speedup while significantly enhancing generation quality, reducing LPIPS from 0.1095 to 0.0316.

Visual counterfactual explanations aim to change classifier decisions through realistic and localized edits while preserving decision-irrelevant content. Existing DDPM-based methods typically perform classifier-guided editing along a long reverse denoising trajectory. The changing noise levels make semantic editability and spatial control difficult to balance, and the editable state is noisy, whereas the target classifier is trained on clean images. As a result, these methods require either costly recursive denoising or low-quality one-step estimates to obtain classifier-facing clean images. We propose FiRe, a Fixed-noise Refinement framework for visual counterfactual explanations. Rather than following a reverse denoising trajectory, FiRe maps the input to a fixed noise level and iteratively refines the noisy state at that level. To provide clean images for classifier guidance, FiRe first adapts Pixel Mean Flow to visual counterfactual explanation, enabling direct clean-image prediction from noisy states. To make fixed-noise refinement produce minimal and localized counterfactual edits, FiRe introduces three FiRe-specific controls: a dynamic dual-mask strategy, adaptive guidance, and early stopping, which determine where edits accumulate, which changes become visible, and when refinement stops. Experiments on five tasks across three datasets show that, compared with the strongest recent baseline, FiRe achieves about 3$\times$ faster online inference and 8$\times$ fewer FLOPs while obtaining comparable or state-of-the-art counterfactual quality.

Large video diffusion models provide rich spatiotemporal priors for autonomous driving, but existing world-action models often inherit the cost of iterative future-video generation even though deployment only requires an ego trajectory. We ask a more basic question: how much of a video diffusion model must be executed to make a reliable driving decision? Through a controlled study of video denoising timesteps and Diffusion Transformer (DiT) depth, we find that planning performance is largely insensitive to the tested video-noise levels, whereas strong trajectories can already be decoded from intermediate layers. Based on this observation, we introduce Adaptive-WAM, a quality-aware multi-exit planner built on a Wan2.2-5B backbone. Trajectory diffusion heads are attached to selected DiT blocks, and a lightweight trajectory-quality scorer terminates inference once the best trajectory decoded so far satisfies a quality threshold; otherwise, computation continues from the cached hidden state to a deeper exit. The deployed planner therefore avoids the iterative classifier-free denoising loop and VAE decoding required for future-video synthesis, while dynamically allocating backbone depth according to trajectory quality. On NAVSIM, the adaptive single-trajectory planner achieves 90.8 PDMS; a separate fixed-exit variant reaches 92.6 PDMS with 64 proposals. It further obtains 89.9 EPDMS on NAVSIM v2, yielding the best reported results among the compared front-view video world-model planners. Without target-domain fine-tuning, Adaptive-WAM transfers to nuScenes with 0.88 m average L2 error and a 0.08% collision rate. On an A100, adaptive routing improves PDMS from 90.62 to 90.79 while averaging 170 ms end-to-end planning latency, approximately 10% below the 190 ms fixed block-15 planner and 47% below the 320 ms fixed full-depth planner. Code will be released.

Flow-matching vision-language-action (VLA) models such as pi0 generate robot actions by integrating a learned denoising velocity field, and have been reported to resist adversarial perturbations that readily fool autoregressive VLAs. We show that this robustness is largely illusory: it stems from prior attacks ignoring the multi-step denoising ODE. We introduce DRIFT (Denoising Redirection via Input perturbation of the Flow-matching Trajectory), a test-time universal adversarial patch placed on the robot's gripper that attacks the denoising velocity field of an off-the-shelf policy. Our central finding is counterintuitive: attacking only the first denoising step is both stronger and cheaper than attacking a wider window of steps, which we explain through a gradient conflict unique to input-space optimization and which is exactly opposite to the training-time backdoor regime. On pi0 and pi0.5 across four LIBERO suites, DRIFT breaks essentially all originally-solvable tasks with a small single patch, far exceeding action- and embedding-space attack baselines.

Text-to-image diffusion models can generate individual concepts well, but they often omit or merge concepts incorrectly with multiple concepts. We trace these failures to an early coordination bottleneck: before denoising begins, prompt-conditioned attention may allocate different concepts to strongly overlapping spatial support, which can keep their attention coupled as denoising proceeds. This observation motivates treating compositional generation as a boundary-condition problem rather than repeatedly controlling the evolving trajectory. To this end, we propose Rectify-then-Diffuse (RTD), a training-free framework that rectifies the initial allocation once before standard denoising. Firstly, we propose Soft-Overlap Disentanglement (SOD), which converts normalized overlap between pilot concept maps into a differentiable and layout-agnostic separation objective. Secondly, we introduce Isotropic Gradient Rectification (IGR), which normalizes the SOD gradient and applies a bounded latent displacement with a consistent scale across prompts and initializations. Extensive experiments show that RTD achieves state-of-the-art compositional fidelity and robust gains. On the AE-Bench object pair subset, RTD improves BLIP-VQA by 45.8% and ImageReward by 19.6% over CO3 while running 2.3$\times$ faster. Code will be released at https://github.com/Z-yiwei/rectify-then-diffuse

Rectified-flow-based diffusion transformers, particularly FLUX, have demonstrated outstanding performance in high-quality image generation. However, achieving fast and accurate inversion--transforming images back to latent noise for faithful reconstruction and editing--remains a challenging bottleneck due to the discretization errors of linear solvers. This paper introduces SlerpFlow, a straightforward yet highly effective zero-shot approach that unlocks the full potential of FLUX for high-fidelity inversion and editing. Unlike existing approaches (e.g., RF-Solver) that rely on complex numerical approximations such as high-order Taylor expansions to correct trajectory errors, we present a geometric view based on the Manifold Hypothesis: the empirically observed trajectory curvature is not a numerical artifact, but rather serves as a necessary "centripetal force" that constrains the flow to remain on the data manifold. Guided by this insight, SlerpFlow integrates Spherical Linear Interpolation (Slerp) to rectify flow velocity directions on the hypersphere, strictly adhering to the intrinsic curvature of the latent space. Crucially, by caching the corrected velocity for subsequent steps, SlerpFlow achieves high-precision inversion while maintaining the computational efficiency of a first-order Euler solver. Extensive experiments on FLUX-based reconstruction and editing tasks demonstrate that SlerpFlow improves reconstruction fidelity and achieves stronger semantic alignment in editing without requiring additional training. Code is available at https://github.com/0answer0/SlerpFlow.

In rectified-flow-based generative models, the neural network can be trained to predict two different targets, such as the instantaneous velocity or the data endpoint, to perform denoising. Although prior work shows that these parameterizations lead to different empirical behaviors, the mechanisms underlying their respective advantages remain to be underexplored, and how to combine them effectively is still unclear. In this work, we analyze how learning errors from different parameterizations affect the generation performance. We show that predicting the data endpoint has a clear training signal that stabilizes training, whereas predicting the velocity maintains stable sampling dynamics near the data manifold. Motivated by these insights, we propose Self-Consistent Flow (SC-Flow), a new method that unifies the benefits of both parameterizations. By employing a lightweight consistency loss, SC-Flow jointly trains a single network to predict both the local velocity and the data endpoint, and the consistency between the two predictions improves the model's performance. The method requires no major architectural changes and adds minimal computational overhead. Extensive experiments on image generation tasks demonstrate that SC-Flow substantially stabilizes optimization and improves the straightness of generation paths, leading to significant gains in generation quality over standard rectified-flow baselines.

Text-to-image (T2I) diffusion models have achieved striking progress but still struggle to synthesize rare concepts involving unusual attribute-object pairings, often resulting in concept omission or semantic drift where a dominant entity overwhelms the generation. Tracing these failures to a lack of compositional balance during the denoising trajectory, we propose RADIANCE, a training-free framework that treats inference as a closed-loop feedback process. RADIANCE augments pretrained backbones with three modular components: (1) a Compositional Similarity Monitor (CSM) that tracks the emergence of objects and attributes in intermediate latents via CLIP-based feedback; (2) a Bidirectional Scale Controller (BSC) that applies a reactive "restoring force" using positive and negative IP-Adapter scales to rebalance biased trajectories; and (3) a Feedback Guidance Scheduler (FGS) that coordinates these updates across timesteps without additional training. We further extend the framework to multi-object prompts via Delayed Adapter Activation (DAA) and Layer-wise Alternating Guidance (LAG) to prevent premature concept fusion. By overlapping monitoring and denoising through pipelined execution, RADIANCE maintains competitive latency while significantly enhancing the per-sample success rate and effective throughput. Experiments on RareBench and T2I-CompBench demonstrate that RADIANCE consistently enhances compositional alignment and perceptual quality over state-of-the-art baselines.

Text-guided diffusion inversion is central to image editing, where an image is mapped to an initial latent and then edited by replaying the denoising process under a modified prompt. In practice, however, inversion is often performed with a lower classifier-free guidance(CFG) scale than the one used for generation or editing. This mismatch is empirically useful but leaves a basic question unresolved: when a target image is generated by a high-CFG trajectory, when can that trajectory actually be inverted? We study this question in a controlled generation--inversion--reconstruction setting, where the true initial latent and denoising trajectory are known. Using prompts taken from an existing diffusion-editing benchmark, we generate images under high CFG and reconstruct them with fixed-point inversion using the same prompt and guidance setting. The results reveal three types of prompt-level reconstruction behavior: easy prompts that reconstruct for most initial latents, hard prompts that fail for most initial latents, and intermediate prompts whose success depends on the prompt--latent pairing. To analyze the generation side, we define prompt pressure, a step-wise measure of how strongly CFG moves the denoising update away from the unconditional trajectory. Total pressure correlates with reconstruction quality and separates easy from hard prompts, but it does not explain the success or failure of intermediate prompt--latent pairs. Text-side analyses further show that the main visual subject and wording can change inversion difficulty. Finally, we evaluate a compact trajectory-consistency intervention that relaxes guidance only at locally unstable inverse steps. This diagnostic check improves reconstruction and Prompt-to-Prompt editing in our controlled setting, supporting the view that high-CFG inversion failure requires local, trajectory-aware analysis.

Diffusion and flow-based generative models produce strong images, yet their controllability remains largely endpoint-centric: users specify conditions and receive final outputs, while the intermediate generative dynamics remain hidden. Recent methods have begun to exploit generation order and process decomposition to improve sample quality, but still treat intermediate states as internal computation rather than objects for interaction. We propose Trajectory Forcing (TF), a trajectory-centric framework that makes the generation path explicit, semantic, and editable. TF organizes synthesis as a sequence of semantically structured stages, progressing from global layout to object-, part-, and detail-level representations. Each stage produces a decodable latent state that can be inspected, evaluated, and locally edited before the next stage begins. To instantiate this path, we derive coarse-to-fine teacher hierarchies by clustering pretrained visual representations such as DINOv2, and train a hierarchy-conditioned one-step flow-matching model at each level. We further introduce trajectory-aware metrics that measure structural consistency and local controllability beyond endpoint quality metrics such as FID. Experiments show that TF achieves competitive sample quality while exposing coherent intermediate states and supporting localized edits across semantic levels. By shifting the focus from final images to the generative path itself, TF opens a route toward controllable, trajectory-aware image synthesis.

Text-to-video (T2V) diffusion models have made it increasingly easy to synthesize realistic and temporally coherent videos, while recent personalization techniques allow such models to imitate a specific subject, style, or motion pattern from only a few reference clips. This capability creates a new data-misuse risk: videos shared online can be collected and used for unauthorized T2V fine-tuning. Existing protective perturbations are mainly designed for image recognition or text-to-image personalization, and therefore focus on corrupting static appearance cues rather than the temporal denoising dynamics that make video personalization possible. To address this gap, we introduce ChronoLock, the first proactive protection framework that makes released videos difficult to exploit for unauthorized T2V personalization. ChronoLock targets the motion-learning process directly by optimizing bounded perturbations over temporal denoising trajectories. It first disrupts intra-chunk temporal adaptation with a diffusion objective that combines fitting error, frame-relative denoising relations, and adjacent-frame variation, and then enlarges inter-chunk boundary mismatch to weaken long-range motion continuity. Transformation-sampled updates further improve robustness to common preprocessing operations.Experiments on UCF Sports and HMDB51 with popular T2V backbones and personalization scheme show that ChronoLock effectively reduces motion imitation under automatic metrics and human evaluation.

Diffusion models are typically trained with objectives that focus on local denoising targets at individual time steps (or adjacent pairs), which do not enforce consistency between predictions along the denoising trajectory. This lack of cross-time consistency can degrade performance, especially for few-step samplers. We introduce a temporal difference (TD) objective that penalizes inconsistency of the model's multi-step progress along the denoising path. By reformulating the diffusion process as a Markov reward process and casting denoising as a policy evaluation problem in reinforcement learning, we derive a unified TD approach that applies to both discrete- and continuous-time diffusion formulations. We further propose a principled sample-based reweighting method that stabilizes training. Empirically, we show that using our TD training can significantly improve sample quality measured by FID, with stronger advantages when the number of sampling steps is small, highlighting its practical utility under low-computation-budget scenarios. We provide ablation studies to justify our design choices, including pairwise loss reweighting, regularization weight, and one-step stride. Overall, our TD approach can be a general drop-in that enforces cross-time consistency and improves generation quality across different diffusion generative models.

Learning-based motion planners, despite recent progress, often suffer from temporal inconsistency. Small perturbations across frames can accumulate into unstable trajectories, degrading comfort and safety in closed-loop driving. Several methods attempt to inject history as a static conditioning signal to stabilize outputs, only to induce the planner to copy historical patterns instead of adapting to environment contexts. To address this limitation, we propose Diffusion Forcing Planner (DFP), a diffusion-based planning framework driven by history-guided control. Specifically, DFP decomposes the full trajectory into history, current and future segments, and assign independent noise levels to each segment. The model jointly denoises the historical and the future segments, enforcing a heterogeneous joint diffusion process. At inference, classifier-free guidance (CFG) is applied to steer future sampling using annealed history in a controllable manner. Closed-loop evaluation and comprehensive ablations on nuPlan show that DFP achieves competitive performance while producing continuous, stable, and controllable motion plans in complex driving scenarios.

This submission documents the divide-and-conquer modeling strategy developed for the CTF-4-Science Lorenz Chaotic Systems Challenge at AI-DEEDS 2026. The challenge uses the CTF-4-Science Lorenz benchmark to evaluate chaotic-system prediction across twelve hidden scores and five scenario families: clean forecasting, noisy reconstruction, noisy-input forecasting, few-shot learning, and parametric generalization. Rather than forcing one model class to handle all regimes, the final system matched each prediction block to the evaluation behavior of its task group. The main contributions are: smoothing-based reconstruction for noisy full-trajectory denoising; NG-RC/NVAR models tuned for noisy long-time attractor forecasting; a fitted Lorenz transition correction restricted to the sensitive clean short-time prefix; and a parametric prefix blend for the interpolation task. The resulting system with final public score of 79.63 shows that bounded, scenario-specific updates can outperform broad model replacement on mixed chaotic forecasting benchmarks.

World Action Models (WAMs) generalize better than standard Vision-Language-Action (VLA) policies to novel motions and environments, because a video-modeling objective lets them learn from abundant unlabeled video rather than scarce labeled robot demonstrations. This generalization is computationally expensive. To complete a task, a WAM runs over multiple inference chunks, and each chunk requires a costly denoising process. Existing acceleration methods reduce this cost by caching and reusing computation within a single chunk's denoising trajectory. Our empirical analysis reveals a substantial source of redundancy they overlook: redundancy across chunks. When a robot executes a smooth behavior, the residuals computed at a given denoising step are strongly correlated from one chunk to the next. We introduce C$^3$ache, a training-free method that caches and reuses these residuals across inference chunks at the same denoising step. Experiments on benchmarks with a Fast-WAM backbone show that C$^3$ache achieves up to a $2.5\times$ speedup in total wall-clock inference time, with negligible degradation in task success rate.

Standard diffusion models corrupt an entire sample with a single shared noise level, forcing all spatial regions to follow the same denoising trajectory. We introduce AsyncPatch Diffusion, a joint-diffusion framework that assigns distinct noise levels to different input dimensions, such as image pixels, or latent tokens. We show how this asynchronous corruption defines a valid generative process while supporting a richer family of spatially heterogeneous denoising trajectories, and prove the first valid ELBO for this process. We show that a single pretrained model can perform spatially adaptive generation, where different regions are denoised on different schedules. A key challenge is training: naive independent noise-level sampling overemphasizes highly heterogeneous configurations and underrepresents homogeneous noise levels, that are crucial during sampling. We address this with a controlled noise-level sampler that regulates both the average corruption level and its spatial variability. AsyncPatch achieves generation quality comparable to conventional diffusion on ImageNet 256 and LSUN, while being natively suited for inpainting without task-specific fine-tuning. We further introduce input guidance, which uses clean or partially corrupted regions to guide the generation of unknown regions, improving local consistency and texture matching. Finally, we demonstrate adaptive generation strategies including uncertainty-guided acceleration and autoregressive sampling.

Image-to-Video diffusion models leverage input images to generate visually stunning content, yet frequently produce motion that violates physical laws. We reveal a surprising finding: a 2-step generation often exhibits better physical consistency than a 50-step output from the same model. Through spectral analysis, we trace this to phase erosion during denoising; the phase degrades significantly (dropping by $\approx 18\%$ from step 2 to step 50), whereas the magnitude remains relatively stable. Building on this insight, we propose PhaseLock, a training-free framework that preserves the valid motion priors from few-step inference throughout the denoising trajectory. Rather than relying on full-step inference for physical consistency, PhaseLock extracts a motion prior from just 2 steps and enforces it onto high-fidelity generation via Latent Delta Guidance. Our approach effectively mitigates phase degradation, improving physical consistency by an average of 6.2 points across diverse models while largely maintaining visual fidelity, with negligible overhead ($1.06\times$ time, $1.02\times$ memory) and reduced reliance on expensive external guidance methods ($\sim5\times$ time). Project Page: https://dnwjddl.github.io/phaselock

Diffusion large language models (dLLMs) generate responses by iteratively unmasking and revising many positions in parallel. This process leaves a rich denoising trace depicting which tokens become confident, which remain unstable, and when commitments form. Existing dLLM reinforcement learning methods use this signal only weakly. Flat rollouts are cheap, but assign a single outcome reward to the whole trajectory. Tree rollouts provide finer, verifiable training signals by branching partial trajectories and propagating leaf rewards upward, but are compute intensive. We ask whether the denoising trace itself can provide tree-like supervision without tree-level compute. We introduce CAPR (Cached-Amortized Path Refinement), a dLLM-RL algorithm that summarizes the denoising trace into a compact path state, uses cached trajectory states to generate cheap sibling continuations, and trains a block-level value head for local block-wise supervision. Under a block-wise unmasking schedule, CAPR records path-state and block-progress features, then redistributes the final outcome reward across blocks according to the tokens revealed in each block. This trains the value head to convert one sparse reward into block-level PPO weights. CAPR therefore recovers much of the granularity of tree search while avoiding full tree expansion, reducing rollout-generation cost to roughly 0.75x that of flat rollouts and 0.6x that of tree rollouts (under standard settings). Across 4x4 Sudoku, Countdown, GSM8K, and Math500, on dense and mixture-of-experts LLaDA backbones, CAPR sets a new state of the art for RL-tuned dLLMs at 256- and 512-token budgets. On Sudoku, it matches the strongest tree-structured baseline at less than one third of the per-step compute.

Text-to-video (T2V) generation faces challenging questions when generating videos with long horizons containing multiple events. Inspired by the intrinsics of the diffusion process, we probe video diffusion transformers (DiTs) and uncover intrinsic turning points in the DiT denoising trajectory where conditioning text affects generation from global layout to fine-grained details. Building on this finding, we present TunerDiT, a simple yet effective progressive steering method that requires no additional training for multi-event generation. TunerDiT comprises two steering handles: (1) Event-Partitioned Masking that enforces event boundaries while allowing cross-event transition bands; (2) Cross-Event Prompt Fusion that injects neighboring event semantics for late-stage refinement. We contribute a self-curated prompt suite for benchmarking multi-event generation, i.e., Meve. TunerDiT achieves state-of-the-art performance across 8 metrics and offers a tunable trade-off between video consistency and event separation, compared with other training-free methods. The improvement in text alignment increases with the event count, indicating a scaling possibility with increasing event count.

Diffusion-based large language models (dLLMs) support parallel text generation via iterative denoising, yet inference remains latency-heavy because many steps are spent on redundant refinement and repeated remasking of tokens whose final values are already determined. Prior acceleration methods mainly depend on step-local confidence heuristics or fixed schedules, which are sensitive to prompt and task variation and ignore strong positional effects within a sequence. We cast diffusion decoding as a dynamic control problem and show that token-wise denoising trajectories provide the key signal for reliable control. We propose a trace-aware decoding framework with two components. First, Temporal-Spatial Parallel Decoding (TSPD) uses a lightweight temporalspatial controller that consumes per-token trajectory features, including confidence, entropy, and momentum, together with token position, to decide when a token has converged and can be safely fixed. Second, we introduce Confidence Extrapolation (CE), a training-free state-space module that forecasts future logit trends with uncertainty to support proactive decisions, including safe look-ahead and targeted stabilization when trajectories are oscillatory or underconfident. Together, TSPD and CE reduce unnecessary denoising iterations while preserving output quality, and they compose cleanly with system optimizations such as KV caching.

Diffusion-based and iterative methods have become effective tools for solving imaging inverse problems. Their reconstruction process naturally forms a trajectory of intermediate estimates. Although these intermediate estimates define a reconstruction trajectory, most methods do not explicitly regularize the transitions between consecutive states. To address this limitation, we introduce TRACE, a training-free TRAjectory-Constrained rEconstruction framework that stabilizes the reconstruction path by coupling adjacent states along the trajectory. This gives a trajectory-level model that can be interpreted as a sequence of proximal updates. Since the exact proximal update is generally intractable, we approximate it with a neural mapping. This yields a diffusion-like reconstruction process with an explicit coupling between neighboring states. We provide a stability analysis showing that temporal coupling bounds trajectory variation and that this control is preserved under untrained network updates. Experiments on linear and nonlinear image reconstruction tasks show that TRACE improves reconstruction quality. Trajectory-level analyses and ablations confirm that temporal coupling directly affects state transitions along the reconstruction path.

Current open-source diffusion models struggle to generate stable and synchronized audio-visual content, particularly in scenarios demanding complex semantic reasoning. The root cause is that existing methods rely on coarse text embeddings from off-the-shelf encoders to guide audio-video denoising, which discards fine-grained semantics and, critically, lacks a shared long-horizon plan, leading to uncoordinated denoising trajectories and fragile cross-modal alignment. We propose Baton, the first framework that introduces explicit semantic planning into joint video-audio generation. Our key insight is that complementing coarse text guidance with semantically rich, modality-aware planned tokens, jointly reasoned and mutually aligned before denoising, can simultaneously restore fine-grained semantic detail and establish a shared blueprint that coordinates both audio and video denoising trajectories. Concretely, Baton first introduces the VA-Planner, a multimodal language model equipped with dual semantic alignment towers, where learnable queries cross-attend to both video and audio features to produce a pair of semantically aligned video and audio planned tokens as keyframe-level blueprints. These planned tokens are injected into the diffusion backbone via cross-attention layers, providing temporally grounded guidance complementary to coarse text embeddings. Since planned tokens do not share one-to-one spatial-temporal correspondence with diffusion latents, we further propose Relative Semantic RoPE, a relative positional encoding that maps planned tokens and latents into a shared spatial-temporal coordinate frame, enabling each latent to accurately attend to its positionally corresponding semantic cues. Experiments on benchmarks show the effectiveness of Baton both qualitatively and quantitatively.

Diffusion Transformers require repeated denoiser evaluations during iterative sampling, making inference computationally expensive. Cache-based acceleration reduces this cost by reusing intermediate representations across denoising steps, but can introduce representation deviations and degrade generation quality. In this paper, we analyze these deviations and show that effective calibration should consider both the direct mismatch caused by reuse and the subsequent trajectory shift induced by earlier corrections. To address this challenge, we propose Trajectory-Consistent Calibration (TCC), a training-free method that calibrates cached representations toward their full-computation counterparts. Specifically, rather than estimating all calibration priors from a single uncorrected cache trajectory, TCC uses an offline iterative procedure so that each prior accounts for the trajectory shift induced by preceding calibrations. Experiments on PixArt-alpha and DiT-XL/2 show that TCC consistently improves FID across representative cache-based acceleration methods while preserving their underlying reuse policies. Notably, in a representative PixArt-alpha cache-acceleration setting based on FORA, TCC reduces FID from 29.83 to 27.35, slightly surpassing the full-computation baseline.

Diffusion and rectified flow (RF) models generate high-fidelity images and videos, but their iterative velocity-field evaluations are computationally expensive. Existing caching methods accelerate sampling by skipping timesteps, yet their coarse approximations introduce accumulated errors over long skip intervals and degrade quality under aggressive acceleration. We propose TACache (Trajectory-Aware Cache), a training-free acceleration framework following a skip-then-compensate paradigm. TACache performs an orthogonal decomposition of discrete velocity acceleration along the RF trajectory into a parallel component and an orthogonal residual, isolating the magnitude and directional sources of per-step approximation error. The framework operates in two stages: offline, cumulative variation thresholds on the magnitude and direction indicators yield the skip schedule and bound how far each skip interval may extend; online, at each skipped step the offline statistics are combined with the sample's historical orthogonal direction to reconstruct the skipped velocity without additional model evaluations. Experiments on BAGEL, FLUX.1-dev, and Wan2.1-1.3B show that TACache achieves up to 4.14 speedup on text-to-image generation and 2.11 speedup on text-to-video generation, with consistent improvements over prior cache-based methods on all reference-based fidelity metrics. Code will be released soon.

Despite strong image-generation performance, diffusion models' reconstruction objectives limit alignment with human preferences. RL enables such alignment through explicit rewards. However, most studies apply RL to the full denoising trajectory, making it computationally costly and weakening preference alignment, i.e., doing more but achieving less. We observe that the impact of RL fine-tuning varies significantly across denoising stages. In the early stage, image structures are unstable and distant from the final reward signal. Applying RL at this stage leads to delayed rewards and action-reward mismatching, resulting in high variance and inefficient updates. Conversely, in the later stage, reward gains saturate, and continued training tends to overfit local details, intensifying reward hacking. To tackle these challenges, we propose AdaScope, an RL-enhanced plug-in that improves generation quality while reducing computational cost. Specifically, AdaScope adaptively identifies the optimal intervention timing for RL by perceiving the structural evolution and semantic consistency during denoising, and dynamically terminates training once the denoising converges and reward gains saturate. As a result, it achieves a rare 'dual benefit': a reduction in computational costs alongside a significant performance improvement. We offer theoretical grounds for the design of AdaScope. Compared with state-of-the-art methods, AdaScope improves performance by 66% while cutting computational cost by 59%.

Recent diffusion- and flow-based VTON methods achieve strong results with pretrained generative models, but their reliance on multi-step sampling incurs high inference cost, while existing acceleration methods largely overlook the intrinsic structure of the try-on task. In this paper, we highlight a key observation: VTON outputs are highly constrained by the conditional inputs, suggesting that the conditional sampling trajectory can be much straighter than that in general image generation, making one-step generation a natural solution. However, limited task-specific data makes training from scratch impractical, forcing existing methods to fine-tune pretrained models whose objectives do not encourage such straight conditional trajectories. Thus, the deviation from an ideal straight path mainly comes from the mismatch between pretrained base models and the conditional nature of try-on generation, rather than from the task itself. Motivated by this insight, we encourage straighter VTON sampling trajectories through three targeted modifications: pure conditional transport, a garment preservation loss, and a self consistency loss. We further introduce a one-step distillation stage. Extensive experiments show that our method achieves state-of-the-art performance with one-step sampling, establishing a new standard for efficient and high-quality VTON.

Diffusion-based trajectory planners can synthesize rich, multimodal robot motions, but their iterative denoising makes online planning and control prohibitively slow. Existing accelerations either modify the sampler or compress the network--sacrificing plan quality or requiring retraining without accounting for downstream control risk. We address the problem of making diffusion-based trajectory planners fast enough for real-time robot use without retraining the model or sacrificing trajectory quality, and in a way that works across diverse state-space diffusion architectures. Our key insight is that diffusion trajectory planners expose two signals we can exploit: a cheap probe of how their internal trajectory representation changes across steps, and analytic coefficients that describe how denoiser errors affect the sampler's state update. By calibrating the first signal against the second on offline runs, we obtain a per-step score that upper-bounds how far the final trajectory can deviate when we reuse a cached denoiser output, and we treat this bound as an uncertainty budget that we can spend over the denoising process. Building on this insight, we present Muninn, a training-free caching wrapper that tracks this uncertainty budget during sampling and, at each diffusion step, chooses between reusing a cached denoiser output when the predicted deviation is small and recomputing the denoiser when it is not. Across standard benchmarks Muninn delivers up to 4.6x wall-clock speedups across several trajectory diffusion models by reducing denoiser evaluations, while preserving task performance and safety metrics. Muninn further certifies that cached rollouts remain within a specified distance of their full-compute counterparts, and we validate these gains in real-time closed-loop navigation and manipulation hardware deployments. Project page: https://github.com/gokulp01/Muninn.

Existing preference datasets for text-to-image models typically store only the final winner/loser images. This representation is insufficient for rectified flow (RF) models, whose generation is naturally indexed by a specific prior noise sample and follows a nearly straight denoising trajectory. In contrast, prior DPO-style alignment for diffusion models commonly estimates trajectories using an independent forward noising process, which can be mismatched to the true reverse dynamics and introduces unnecessary variance. We propose Prior Noise-Aware Preference Optimization (PNAPO), an off-policy alignment framework specialized for rectified flow. PNAPO augments preference data by retaining the paired prior noises used to generate each winner/loser image, turning the standard (prompt, winner, loser) triplet into a sextuple. Leveraging the straight-line property of RF, we estimate intermediate states via noise-image interpolation, which constrains the trajectory estimation space and yields a tighter surrogate objective for preference optimization. In addition, we introduce a dynamic regularization strategy that adapts the DPO regularization based on (i) the reward gap between winner and loser and (ii) training progress, improving stability and sample efficiency. Experiments on state-of-the-art RF T2I backbones show that PNAPO consistently improves preference metrics while substantially reducing training compute.

Score Distillation Sampling (SDS) and its variants have been widely used for text-to-3D generation by distilling 2D image diffusion priors. However, the standard SDS objective is prone to severe mode collapse, frequently yielding over-smoothed and over-saturated results. Although recent advancements, such as Score Distillation via Inversion (SDI), mitigate these artifacts and produce visually sharper models, they ultimately fail to faithfully capture the full target distribution. In this work, we show that the bottleneck limiting the sampling capacity of SDI stems from its reliance on the posterior mean estimator, which is mathematically equivalent to a single-step Euler approximation of the deterministic reverse DDIM trajectory. To address this, we propose a naturally motivated extension termed Probability-Flow Distillation (PFD). We establish that PFD corresponds exactly to a Wasserstein gradient flow, thereby inducing principled distribution-matching dynamics. Finally, we show that PFD can synthesize 3D assets with fine-grained, high-fidelity details and achieve improved quality compared to existing methods.

Diffusion-based models decompose sampling into many small Gaussian denoising steps -- an assumption that breaks down when generation is compressed to a few coarse transitions. Existing few-step methods address this through distillation, consistency training, or adversarial objectives, but sacrifice the likelihood framework in the process. We introduce Normalizing Trajectory Models (NTM), which models each reverse step as an expressive conditional normalizing flow with exact likelihood training. Architecturally, NTM combines shallow invertible blocks within each step with a deep parallel predictor across the trajectory, forming an end-to-end network trainable from scratch or initializable from pretrained flow-matching models. Its exact trajectory likelihood further enables self-distillation: a lightweight denoiser trained on the model's own score produces high-quality samples in four steps. On text-to-image benchmarks, NTM matches or outperforms strong image generation baselines in just four sampling steps while uniquely retaining exact likelihood over the generative trajectory.

Diffusion large language models are a compelling alternative to autoregressive models, yet existing RL methods for diffusion treat all denoising steps as equally important and rely on biased, high-variance likelihood estimates. We identify two fundamental weaknesses: the absence of temporal credit assignment across the denoising trajectory, and the systematic bias of mean-field likelihood estimates used for policy optimization. To address these, we propose Denoising-Aware Credit Assignment for GRPO (DACA-GRPO), a lightweight, plug-and-play enhancement for any GRPO-style trainer. DACA-GRPO introduces two complementary mechanisms: Denoising Progress Scores, which extract per-token importance weights from intermediate predictions at no additional forward cost, and Stratified Masking Likelihood, which partitions token positions into strata so that each token is predicted with most of the sequence as context, reducing the mean-field bias. Applied on top of three GRPO base methods, DACA-GRPO achieves consistent improvements across seven benchmarks spanning mathematical reasoning, code generation, constraint satisfaction, and constrained generation, with gains of up to 5.6pp on math reasoning, 7.4pp on code generation, 36.3pp on constraint satisfaction, and 5.9pp on JSON schema adherence.

Representation alignment has recently emerged as an effective paradigm for accelerating Diffusion Transformer training. Despite their success, existing alignment methods typically impose a fixed supervision target or a fixed alignment granularity throughout the entire denoising trajectory, whether the guidance is provided by external vision encoders, internal self-representations, or VAE-derived features. We argue that such timestep-agnostic alignment is suboptimal because the useful granularity of representation supervision changes systematically with the signal-to-noise ratio. In high-noise regimes, diffusion models benefit more from coarse semantic and layout-level anchoring, whereas in low-noise regimes, the training signal should emphasize spatially detailed and structurally faithful refinement. This non-stationary alignment behavior creates a representational mismatch for static single-level supervisors. To address this issue, we propose Adaptive Hierarchical Prior Alignment (AHPA), a lightweight alignment framework that exploits the hierarchical representations naturally embedded in the frozen VAE encoder. Instead of using only a single compressed latent as the alignment target, AHPA extracts multi-level VAE features that provide complementary priors ranging from local geometry and spatial topology to coarse semantic layout. A timestep-conditioned Dynamic Router adaptively selects and weights these hierarchical priors along the denoising trajectory, thereby synchronizing the alignment granularity with the model's evolving training needs. Extensive experiments show that AHPA improves convergence and generation quality over baselines and incurs no additional inference cost while avoiding external encoder supervision during training.

Diffusion models are a leading paradigm for data generation, but training-free editing typically re-runs the full denoising trajectory for every edit strength, making iterative refinement expensive. To address this issue, we instead edit near the data manifold, where small local updates can replace repeated re-synthesis. To enable this, we estimate a local manifold tangent space directly from perturbed samples and prove that this sample-based estimator closely approximates the true tangent. Building on this guarantee, we devise a Jacobian-free algorithm that constructs a tangent frame via small perturbations to the initial noise and alternates small tangent moves with diffusion-based projections. Updates within this frame follow principled on-manifold directions while suppressing off-manifold drift, enabling fine-grained edits without full re-diffusion or additional training. Edit strength is controlled by the number of steps for rapid, continuous adjustments that preserve fidelity and plug into existing samplers. Empirically, the resulting tangent directions yield smooth, semantic unsupervised traversals and effective CLIP-guided optimization, demonstrating practical interactive continuous editing.

Diffusion language models expose an explicit denoising trajectory, making it possible to ask when different kinds of information become measurable during generation. We study three independent 32-step runs of LLaDA-8B-Base on masked WikiText-103 text, each with 1{,}000 probe-training sequences and 200 held-out evaluation sequences. From saved trajectories, we derive four temporal measurements: token commitment; linear recoverability of part-of-speech (POS), coarse semantic category, and token identity; confidence and entropy dynamics; and sensitivity under mid-trajectory re-masking. Across seeds, the same ordering recurs: content categories stabilize earlier than function-heavy categories, POS and coarse semantic labels remain substantially more linearly recoverable than exact lexical identity under our probe setup, uncertainty remains higher for tokens that ultimately resolve incorrectly even though late confidence becomes less calibrated, and perturbation sensitivity peaks in the middle of the trajectory. A direct/collateral decomposition shows that this peak is overwhelmingly local to the perturbed positions themselves. In this LLaDA+WikiText setting, denoising time is therefore a useful analysis axis: under our measurements, coarse labels are recovered earlier and more robustly than lexical identity, trajectory-level uncertainty tracks eventual correctness, and mid-trajectory states are the most intervention-sensitive.

Reinforcement learning, particularly Group Relative Policy Optimization (GRPO), has emerged as an effective framework for post-training visual generative models with human preference signals. However, its effectiveness is fundamentally limited by coarse reward credit assignment. In modern visual generation, multiple reward models are often used to capture heterogeneous objectives, such as visual quality, motion consistency, and text alignment. Existing GRPO pipelines typically collapse these rewards into a single static scalar and propagate it uniformly across the entire diffusion trajectory. This design ignores the stage-specific roles of different denoising steps and produces mistimed or incompatible optimization signals. To address this issue, we propose Objective-aware Trajectory Credit Assignment (OTCA), a structured framework for fine-grained GRPO training. OTCA consists of two key components. Trajectory-Level Credit Decomposition estimates the relative importance of different denoising steps. Multi-Objective Credit Allocation adaptively weights and combines multiple reward signals throughout the denoising process. By jointly modeling temporal credit and objective-level credit, OTCA converts coarse reward supervision into a structured, timestep-aware training signal that better matches the iterative nature of diffusion-based generation. Extensive experiments show that OTCA consistently improves both image and video generation quality across evaluation metrics.

This paper focuses on the alignment of flow matching models with human preferences. A promising way is fine-tuning by directly backpropagating reward gradients through the differentiable generation process of flow matching. However, backpropagating through long trajectories results in prohibitive memory costs and gradient explosion. Therefore, direct-gradient methods struggle to update early generation steps, which are crucial for determining the global structure of the final image. To address this issue, we introduce LeapAlign, a fine-tuning method that reduces computational cost and enables direct gradient propagation from reward to early generation steps. Specifically, we shorten the long trajectory into only two steps by designing two consecutive leaps, each skipping multiple ODE sampling steps and predicting future latents in a single step. By randomizing the start and end timesteps of the leaps, LeapAlign leads to efficient and stable model updates at any generation step. To better use such shortened trajectories, we assign higher training weights to those that are more consistent with the long generation path. To further enhance gradient stability, we reduce the weights of gradient terms with large magnitude, instead of completely removing them as done in previous works. When fine-tuning the Flux model, LeapAlign consistently outperforms state-of-the-art GRPO-based and direct-gradient methods across various metrics, achieving superior image quality and image-text alignment.

Achieving high-fidelity generation in extremely few sampling steps has long been a central goal of generative modeling. Existing approaches largely rely on distillation-based frameworks to compress the original multi-step denoising process into a few-step generator. However, such methods inherently constrain the student to imitate a stronger multi-step teacher, imposing the teacher as an upper bound on student performance. We argue that introducing \textbf{preference alignment awareness} enables the student to optimize toward reward-preferred generation quality, potentially surpassing the teacher instead of being restricted to rigid teacher imitation. To this end, we propose \textbf{Reward-Aware Trajectory Shaping (RATS)}, a lightweight framework for preference-aligned few-step generation. Specifically, teacher and student latent trajectories are aligned at key denoising stages through horizon matching, while a \textbf{reward-aware gate} is introduced to adaptively regulate teacher guidance based on their relative reward performance. Trajectory shaping is strengthened when the teacher achieves higher rewards, and relaxed when the student matches or surpasses the teacher, thereby enabling continued reward-driven improvement. By seamlessly integrating trajectory distillation, reward-aware gating, and preference alignment, RATS effectively transfers preference-relevant knowledge from high-step generators without incurring additional test-time computational overhead. Experimental results demonstrate that RATS substantially improves the efficiency--quality trade-off in few-step visual generation, significantly narrowing the gap between few-step students and stronger multi-step generators.

The recent success of inference-time scaling in large language models has inspired similar explorations in video diffusion. In particular, motivated by the existence of "golden noise" that enhances video quality, prior work has attempted to improve inference by optimising or searching for better initial noise. However, these approaches have notable limitations: they either rely on priors imposed at the beginning of noise sampling or on rewards evaluated only on the denoised and decoded videos. This leads to error accumulation, delayed and sparse reward signals, and prohibitive computational cost, which prevents the use of stronger search algorithms. Crucially, stronger search algorithms are precisely what could unlock substantial gains in controllability, sample efficiency and generation quality for video diffusion, provided their computational cost can be reduced. To fill in this gap, we enable efficient inference-time scaling for video diffusion through latent reward guidance, which provides intermediate, informative and efficient feedback along the denoising trajectory. We introduce a latent reward model that scores partially denoised latents at arbitrary timesteps with respect to visual quality, motion quality, and text alignment. Building on this model, we propose LatSearch, a novel inference-time search mechanism that performs Reward-Guided Resampling and Pruning (RGRP). In the resampling stage, candidates are sampled according to reward-normalised probabilities to reduce over-reliance on the reward model. In the pruning stage, applied at the final scheduled step, only the candidate with the highest cumulative reward is retained, improving both quality and efficiency. We evaluate LatSearch on the VBench-2.0 benchmark and demonstrate that it consistently improves video generation across multiple evaluation dimensions compared to the baseline Wan2.1 model.

Deploying GRPO on Flow Matching models has proven effective for text-to-image generation. However, existing paradigms typically propagate an outcome-based reward to all preceding denoising steps without distinguishing the local effect of each step. Moreover, current group-wise ranking mainly compares trajectories at matched timesteps and ignores within-trajectory dependencies, where certain early denoising actions can affect later states via delayed, implicit interactions. We propose TurningPoint-GRPO (TP-GRPO), a GRPO framework that alleviates step-wise reward sparsity and explicitly models long-term effects within the denoising trajectory. TP-GRPO makes two key innovations: (i) it replaces outcome-based rewards with step-level incremental rewards, providing a dense, step-aware learning signal that better isolates each denoising action's "pure" effect, and (ii) it identifies turning points-steps that flip the local reward trend and make subsequent reward evolution consistent with the overall trajectory trend-and assigns these actions an aggregated long-term reward to capture their delayed impact. Turning points are detected solely via sign changes in incremental rewards, making TP-GRPO efficient and hyperparameter-free. Extensive experiments also demonstrate that TP-GRPO exploits reward signals more effectively and consistently improves generation. Demo code is available at https://github.com/YunzeTong/TurningPoint-GRPO.

Diffusion models generate conditional samples by progressively denoising Gaussian noise, yet the denoising trajectory can stall at visually plausible but low-quality outcomes with conditional misalignment or structural artifacts. We interpret this behavior as local optima in a surrogate quality landscape: Once early denoising commits to a suboptimal global structure, later steps mainly sharpen details and seldom correct the underlying mistake. While existing inference-time approaches explore alternative diffusion states via re-noising with fixed strength or direction, they exhibit limited capacity to escape steep quality plateaus. We propose Controlled Random Zigzag Sampling (Ctrl-Z Sampling),a scalable sampling strategy that detects plateaus in quality landscape via a surrogate score, and allocates exploration only when a plateau is detected. Upon detection, Ctrl-Z Sampling rolls back to noisier states, samples a set of alternative continuations, and updates the trajectory when a candidate improves the score, otherwise escalating the exploration depth to escape the current plateau. The proposed method is model-agnostic and broadly compatible with existing diffusion frameworks. Experiments show that Ctrl-Z Sampling consistently improves generation quality over other inference-time scaling samplers across different NFE budgets, offering a scalable compute-quality trade-off. Code available at: https://github.com/ShunqiM/Ctrl-Z-Sampling.

This work presents an optimization method for generating kinodynamically feasible and collision-free multi-robot trajectories that exploits an incremental denoising scheme in diffusion models. Our key insight is that high-quality trajectories can be discovered merely by denoising noisy trajectories sampled from a distribution. This approach has no learning component, relying instead on only two ingredients: a dynamical model of the robots to obtain feasible trajectories via rollout, and a fitness function to guide denoising with Monte Carlo gradient approximation. The proposed framework iteratively optimizes a deformation for the previous trajectory with the current denoising process, allows anytime refinement as time permits, supports different dynamics, and benefits from GPU acceleration. Our evaluations for differential-drive and holonomic teams with up to 16 robots in 2D and 3D worlds show its ability to discover high-quality solutions faster than other black-box optimization methods such as MPPI. In a 2D holonomic case with 16 robots, it is almost twice as fast. As evidence for feasibility, we demonstrate zero-shot deployment of the planned trajectories on eight multirotors. Code and video: https://github.com/proroklab/d4orm