NeurIPS 2026 Papers

Cyclic peptides are an increasingly important therapeutic modality, offering antibody-like binding specificity within compact and chemically tunable scaffolds. Recent deep generative models have advanced target-specific peptide design, where SE(3)-equivariant diffusion and flow-matching frameworks provide natural inductive biases for peptide-protein complex generation. However, existing SE(3)-based peptide generators mainly focus on linear peptides and do not explicitly control cyclic topology. As shown by recent cyclic peptide benchmarks such as CPSea, current generative baselines still have limited cyclization success and remain weak at controllably generating disulfide- and isopeptide-cyclized peptide distributions. In this work, we propose **CPFlow**, a test-time scaled autoregressive flow-matching framework for receptor-conditioned cyclic peptide sequence-structure co-design. CPFlow autoregressively unmasks residues and predicts full-atom sequence-structure variables with continuous flow matching. By decomposing generation into stepwise flow updates, CPFlow allows each step to balance target binding with structural closure. At inference time, sequence-geometry guided unmasking and multi-particle test-time scaling explore high-confidence autoregressive trajectories beyond the trained model without additional training. Cyclization-aware relative position encodings further enable stable control over head-tail, disulfide, and isopeptide cyclization. Experiments on the CPSea benchmark show that CPFlow outperforms strong generative baselines across *designability* (scRMSD **↓ 0.30 Å**), *self-consistency* (scRMSD **↓ 0.15 Å**), and *binding energy* (mean ΔG **↓ 3.0**), with **93.4%** *binding success* and **0.623** *diversity*. The code for CPFlow is available at https://anonymous.4open.science/r/CPFlow-F226.

Detecting training data memorization in diffusion models is important for copyright protection and privacy auditing. We view memorization as an abnormally local concentration process: during reverse-time generation, a memorized instance acts as a point-like attractor whose probability basin is sharper and more position-sensitive than that of a generalized concept. Starting from the Fokker–Planck equation, we derive an exact evolution law for the score field $\partial_t \mathbf{s}_t$ and show that its leading geometric contribution in score-dominated local regimes is $\mathbf{H}_t \mathbf{s}_t$, linking temporal concentration dynamics to spatial curvature. We then show that standard sampling along a shared guided trajectory already exposes this curvature information through a complementary transport-curvature response, without requiring explicit Hessian computation. Motivated by this analysis, we propose the **Dynamical Singularity Metric (DSM)**, an on-trajectory detector that measures the pathwise score-evolution discrepancy between conditional and unconditional branches. DSM requires no additional backpropagation or network evaluations beyond sampling itself. Experiments on Stable Diffusion show that DSM matches or exceeds curvature-based baselines while being substantially cheaper and effective at the earliest reverse step.

Diffusion language models (DLMs) can generate multiple tokens in parallel, but training large DLMs from scratch remains expensive. A practical alternative is to adapt off-the-shelf autoregressive (AR) checkpoints into diffusion models, reusing their linguistic and reasoning capabilities. Existing adaptation recipes either modify logits and grow attention masks toward full-sequence diffusion, or directly fine-tune ARweights under a block-diffusion objective, leaving two questions underexplored: what diffusion paradigm should AR-to-DLM adaptation target, and what transition path preserves AR knowledge most effectively? We argue that Block-Diffusion is a natural destination because AR decoding corresponds to block size one at the level of attention and generation order, while larger blocks introduce controlled intra-block bidirectionality and parallel generation. Based on this view, we propose a context-causal adaptation path that keeps committed context strictly causal, a one-pass parallel training formulation with auxiliary AR guidance, and a gradual block-size curriculum. Across several AR initializations and model scales, these components improve average adaptation performance over random mask annealing and direct fine-tuning. Scaling the recipe yields NBDIFF-7B, which supports 32K-token contexts and achieves the strongest average performance among the compared diffusion LLM baselines on general, math, and code benchmarks. Code and checkpoints will be released upon publication.

Neural decoders have shown strong potential for error correction in short- and moderate-length regimes, yet a fundamental tension remains between decoding accuracy and inference latency. Recent attempts to leverage diffusion probabilistic models for channel decoding typically adopt a fully generative paradigm, initializing the reverse process from an observation-agnostic prior, which overlooks a key structural property of channel decoding: the received signal already contains substantial information about the target codeword. In this work, we propose Channel Residual Diffusion Model (ChRes-DM), a principled diffusion-based decoding framework that reinterprets channel decoding as a directed restoration process anchored at the noisy observation. Instead of sampling from a generic prior, ChRes-DM constructs a geometric residual bridge between the received signal and the clean codeword, explicitly modeling the conditional transport induced by the channel and leading to a deterministic Probability Flow Ordinary Differential Equation (PF-ODE) that governs the decoding dynamics. By eliminating redundant stochastic sampling inherent in conventional diffusion models, ChRes-DM enables efficient iterative decoding with flexible step-skipping, offering fine-grained control over the accuracy–latency trade-off. Extensive experiments across representative channel coding benchmarks demonstrate that ChRes-DM achieves competitive or superior decoding performance compared to existing neural decoders while significantly reducing inference iterations, highlighting diffusion-based residual transport as a promising and scalable paradigm for neural channel decoding.

Discrete diffusion models have emerged as a promising direction for vision-language tasks, offering bidirectional context modeling and theoretical parallelization. However, their practical application is severely hindered by a train-inference discrepancy, which leads to catastrophic error cascades: initial token errors during parallel decoding pollute the generation context, triggering a chain reaction of compounding errors and leading to syntactic errors and semantic hallucinations. To address this fundamental challenge, we reframe the generation process from passive denoising to active refining. We introduce ReDiff, a refining-enhanced diffusion framework that teaches the model to identify and correct its own errors. Our approach features a two-stage training process: first, we instill a foundational revision capability by training the model to revise synthetic errors; second, we implement a novel online self-correction loop where the model is explicitly trained to revise its own flawed drafts by learning from an expert's corrections. This mistake-driven learning endows the model with the crucial ability to revisit and refine its already generated output, effectively breaking the error cascade. Extensive experiments demonstrate that ReDiff significantly improves the coherence and factual accuracy of generated content, enabling stable and efficient parallel generation far superior to traditional denoising methods.

Flow matching has emerged as a standard paradigm for robotic manipulation owing to its strong expressive power for modelling complex, multimodal action distributions, alongside similar approaches like diffusion policy. However, existing methods rely on discretized action chunks, making them brittle to demonstrations collected at heterogeneous control frequencies and prone to temporally inconsistent actions that degrade control stability. In this paper, we propose Frequency-Aware Flow Matching (FAFM), which outputs continuous, temporally consistent actions. To handle heterogeneous frequency input, we transform discrete action sequences into the frequency domain with the discrete cosine transform (DCT), perform flow matching over the resulting coefficients, and reconstruct continuous actions via cosine basis expansion. To generate temporally consistent actions, we regularize the first-order temporal derivative to promote smooth actions. This corresponds to a Sobolev-type constraint that suppresses high-frequency errors and discourages abrupt action changes. Our FAFM is simple, introduces no additional network parameters and applies to standalone flow-matching policies and vision-language action models. Across synthetic toy benchmark, obstacle avoidance, LapGym, and LIBERO, FAFM improves success rates, multimodal expressivity, motion smoothness, convergence speed, robustness to mechanical bias and mixed-frequency input. These gains are consistent when deployed on a real-world Franka robot. Code available at \url{https://anonymous.4open.science/r/FAFM}.

The application of diffusion transformers is suffering from their significant inference costs. Recently, feature caching has been proposed to solve this problem by reusing features from previous timesteps, thereby skipping computation in future timesteps. However, previous feature caching assumes that features in adjacent timesteps are similar or continuous, which does not always hold in all settings. To investigate this, this paper begins with an analysis from the frequency domain, which reveal that different frequency bands in the features of diffusion models exhibit different dynamics across timesteps. Concretely, low-frequency components, which decide the structure of images, exhibit higher similarity but poor continuity. In contrast, the high-frequency bands, which decode the details of images, show significant continuity but poor similarity. These interesting observations motivate us to propose Frequency-aware Caching (FreqCa) which directly reuses features of low-frequency components based on their similarity, while using a second-order Hermite interpolator to predict the volatile high-frequency ones based on its continuity. Besides, we further propose to cache Cumulative Residual Feature (CRF) instead of the features in all the layers, which reduces the memory footprint of feature caching by 99%. Extensive experiments on FLUX.1-dev, FLUX.1-Kontext-dev, Qwen-Image, and Qwen-Image-Edit demonstrate its effectiveness in both generation and editing. Codes are available in the supplementary materials and will be released on GitHub.

Current 4D occupancy world models use heavy cross-attention or deep recurrence to disentangle ego-motion from scene dynamics. This requires significant computational capacity. However, this effort is largely redundant since ego-motion is inherently known from odometry. We present FreeOcc, a lightweight continuous-time world model that introduces explicit $SE(2)$ geometric decoupling into a conditional flow-matching framework. By mathematically factoring out self-motion, we create a purely dynamic feature space. This space supports attention-free temporal fusion and allows physics-constrained ODEs to operate strictly on residual agent kinematics. To maximize deployment efficiency, FreeOcc introduces an uncertainty-aware blending mechanism. This routes well-observed voxels to a single-pass decoder, reserving the ODE solver exclusively for ambiguous, high-uncertainty regions. Requiring only 28.3M parameters—roughly 40\% of comparable models—our optimal ensemble mode (FreeOcc-E) runs at 27 FPS. On nuScenes, FreeOcc achieves state-of-the-art forecasting performance with a 0.47 m Near Field Chamfer Distance (NFCD) and 32.1\% mIoU. Furthermore, the model transfers zero-shot to SemanticKITTI. It also proves highly robust, retaining 92.8\% of its ideal mIoU under significant sensor packet loss and timestamp jitter.

Diffusion Large Language Models (dLLMs) have emerged as a compelling paradigm for language modeling, offering the unique potential for highly efficient inference via multi-token parallel decoding. However, unlocking this potential remains challenging. High-quality generation typically defaults to one-token-per-step static decoding, while existing parallel algorithms rely on heuristic confidence thresholds, introducing a fragile trade-off between decoding efficiency and generation quality. To overcome this, we introduce **Free** **D**raft-**a**nd-**Ve**rification (**FreeDave**), a novel training-free and model-free fast decoding algorithm. FreeDave capitalizes on the inherent properties of dLLMs by treating future token predictions as "free drafts" and rigorously self-verifying them in subsequent forward passes. Theoretically, FreeDave is guaranteed to use the fewest possible model forward passes to reproduce the exact sequence generated by static decoding, achieving algorithmically lossless acceleration. Extensive evaluations on math reasoning and code generation benchmarks demonstrate that FreeDave can boost the number of generated tokens per model forward (TPF) by up to 5.48$\times$ and tokens per second (TPS) by up to 3.94$\times$, while robustly maintaining generation quality and avoiding the task-specific performance degradation faced by heuristic methods.

Tools from random matrix theory have become central to deep learning theory, using spectral information to provide mechanisms for modeling generalization, robustness, scaling, and failure modes. While often capable of modeling empirical behavior, practical computations are limited by matrix size, often imposing a restriction to models that are too small to be realistic. This motivates the inference of properties of larger models from the behavior of smaller ones. Free decompression (FD) is a recently proposed method for extrapolating spectral information across matrix sizes, but its utility is currently limited by strong assumptions that preclude its implementation on more realistic machine learning (ML) models. We use algebraic spectral curve theory to provide a general FD methodology for spectral densities whose Stieltjes transform satisfies an algebraic relation, a modeling assumption that is more likely to hold in practice. This recasts FD as an evolution along spectral curves which can be readily integrated. Our framework enables the expansion of spectral densities that have multiple or multi-modal bulks, that exist at multiple scales, and that contain atoms, all characteristic of real-world data and popular ML models. We demonstrate the efficacy of our framework on models of interest in modern ML, including Hessian and activation matrices associated with neural networks and large-scale diffusion models.

Large vision-language-action (VLA) policies are increasingly trained as conditional generative models over action chunks, yet they typically improve by imitating the data they are given. This is limiting in deployment, where robots collect mixed-quality experience containing demonstrations, partial completions, recoverable mistakes, and failures. Full behavior cloning imitates failures, filtered behavior cloning discards useful sub-trajectories, and offline RL usually requires a large separate critic. We introduce ForesightFlow, a self-guided flow policy that augments each generated action chunk with a learned success-potential vector. The same flow therefore proposes candidate actions and scores them, enabling best-of-K inference without an external critic. The key challenge is that policy improvement and value calibration require different supervision: advantage weighting should suppress low-quality actions, but applying the same weights to the potential dimension removes the failure gradients needed for calibration. We address this with decoupled advantage-weighted flow matching, applying exponentiated advantage weights only to action velocities while training potential velocities uniformly. We also derive a single-step boundary estimator for conditional flow matching with independent endpoint sampling, allowing advantage computation with one stop-gradient forward pass. Across five BEHAVIOR-1K simulation tasks and five real-world bimanual tasks, ForesightFlow improves over imitation baselines, matches the strongest separate-critic baseline in average simulation success, improves real-world success, and reduces training compute by 38\%. Ablations show that decoupling prevents value hallucination, the one-step estimator preserves candidate-ranking fidelity, and self-guided sampling improves long-horizon performance.

Existing imitation learning methods enable robots to interact autonomously with the physical environment. However, contact-rich manipulation tasks remain a significant challenge due to complex contact dynamics that demand high-precision force feedback and control. Although recent efforts have attempted to integrate force/torque sensing into policies, how to build a simple yet effective framework that achieves robust generalization under multimodal observations remains an open question. In this paper, we propose **ForceFlow**, a force-aware reactive framework built upon flow matching. For contact-stage policy design, we investigate force signal fusion mechanisms and adopt an asymmetric multimodal fusion architecture that treats force as a global regulatory signal, combined with a joint prediction paradigm that enhances the policy's understanding of instantaneous force and historical information, thereby achieving deep coupling between force and motion. For task-level hierarchical decomposition, we divide manipulation into a vision-dominant approach stage (VLM-based pointing for target localization) and a touch-dominant interaction stage (force-driven contact execution), with a Vision-to-Force (V2F) handover mechanism that explicitly decouples spatial generalization from contact regulation. Experimental results across six real-world contact-rich tasks demonstrate that ForceFlow achieves a 37\% success rate improvement over the strong baseline ForceVLA while maintaining significantly lower cost. Moreover, ForceFlow exhibits accurate force signal prediction and demonstrates superior performance in contact force self-regulation and zero-shot out-of-distribution (OOD) generalization.

Existing approaches to controllable generation typically rely on fine-tuning, auxiliary networks, or test-time search. We show that flow matching admits a different control interface: adaptation through examples. For deterministic interpolants, the velocity field is solely governed by a conditional endpoint mean; shifting this mean shifts the flow itself. This yields a simple principle for controllable generation: steer a pretrained model by changing the reference set it follows. We instantiate this idea in two forms. Reference-Mean Guidance is training-free: it computes a closed-form endpoint-mean correction from a reference bank and applies it to a frozen FLUX.2-klein (4B) model, enabling control of color, identity, style, and structure while keeping the prompt, seed, and weights fixed. Semi-Parametric Guidance amortizes the same idea through an explicit mean anchor and learned residual refiner, matching unconditional DiT-B/4 quality on AFHQv2 while allowing the reference set to be swapped at inference time. These results point to a broader direction: generative models that adapt through data, not parameter updates.

Recent advances in autoregressive video diffusion have enabled sequential and streaming video generation. However, long-horizon generation requires increasingly large KV caches, making efficient compression without sacrificing quality challenging. Existing methods mostly select historical frames based on attention scores, but their context decisions remain coarse. When multiple frames are generated in the same chunk, these methods often apply a shared history selection to the whole chunk, score historical frames solely by attention, and assign head-wise budgets either uniformly or by attention-pattern heuristics rather than explicit head-importance estimation. We show that frames within the same generated chunk can depend on distinct historical frames, that the same historical frame can receive different attention scores as its relative temporal distance to the current frames changes, and that masking different heads induces unequal generation degradation. Motivated by these findings, we propose \textbf{Focused Forcing}, a training-free KV selection method that focuses cached history along both generated-frame and head dimensions. For each generated frame, Focused Forcing preserves the most relevant and distinctive historical frames by combining attention scores with diversity scores of historical frames, while assigning larger budgets to heads with higher estimated importance. Across multiple autoregressive generation paradigms, Focused Forcing achieves up to $\textbf{1.48}\times$ end-to-end acceleration without training, while \textbf{improving visual quality and text alignment}. \textit{Our code will be released on GitHub.}

Reference-based image quality assessment (IQA) metrics aim to reflect how humans perceive the perceptual distance between a pair of images. To learn how the human visual system (HVS) operates, recent reference-based IQA metrics heavily rely on human-annotated data. Mean opinion score (MOS)-based pointwise scoring, which assigns a scalar quality value per image, is preferable for annotation but is prohibitively expensive to collect at scale and is known to be noisy due to inconsistent human judgments. As an alternative, two-alternative forced choice (2AFC) pairwise labels have gained popularity due to their reliability and efficiency, but they capture only relative comparisons between pairs. In this paper, we propose a fully automated data generation pipeline that generates pointwise perceptual distance labels between image pairs without any human annotation. Our approach exploits the generative dynamics of diffusion models as a perceptual distance proxy, where the coarse structure of an image is generated in the early timesteps and the fine details are generated in the later timesteps. Images that fork early in the generation process share only coarse structure and are perceptually far apart; images that fork late differ only in fine detail. We demonstrate that the diffusion trajectory aligns well with the human visual system, and use this forking moment, FoMo, as a reference-grounded distance label to supervise the training of a reference-based IQA metric. The pointwise labels, which support universal comparison between arbitrary image pairs, enable an information-rich training objective. Extensive experiments across diverse backbone architectures confirm the effectiveness of our generation pipeline, outperforming human-annotated datasets in multiple benchmarks.

Many inference-time tasks for pretrained discrete diffusion models and diffusion language models reduce to drawing samples from a tilted version of the pretrained distribution. Feynman--Kac sequential Monte Carlo (SMC) makes this correction exact in principle, but its prescribed weights routinely degenerate when the proposal dynamics are misaligned with the tilt, capping the practical gains from additional particles. We introduce *FluxLite*, a lightweight, training-free proposal-control framework for discrete diffusion. On the sparse directed graph of pretrained reverse rates, any sparse jump-rate perturbation can be exactly compensated by a $q_t$-weighted graph-divergence term in the Feynman--Kac potential; the target path is therefore preserved while the residual reweighting variance becomes a local convex objective. We instantiate this principle as two practical samplers: a one-hop local reallocation rule (HEU) and a small nonnegative quadratic program over pretrained-rate bases (D-VCG). We further prove population stability under the standard score-entropy training loss, identifying a tilted-path coverage factor that governs robustness to score error, together with finite-particle convergence for a fixed controlled Feynman--Kac recursion. Empirically, FluxLite improves over standard Feynman--Kac SMC baselines by up to two orders of magnitude in terminal KL on an analytically tractable finite-state CTMC benchmark, and reduces connected-correlation MSE on 2D Ising sampling by $5$--$7\times$ in geometric mean and up to $55\times$ at peak.

Ground-to-space astronomical super-resolution requires recovering space-quality images from ground-based observations that are simultaneously limited by pixel sampling resolution and atmospheric seeing, which imposes a stochastic, spatially varying PSF that cannot be resolved through upsampling alone. Existing methods rely on synthetic training pairs that fail to capture real atmospheric statistics and are prone to either over-smoothed reconstructions or hallucination sources with no physical counterpart in the observed sky. We propose FluxFlow, a conservative pixel-space flow-matching framework that incorporates observation uncertainty and source-region importance weights during training, and a training-free Wiener-regularised test-time correction to suppress hallucination sources while preserving recovered detail. We further construct the DESI--HST Dataset, the large-scale real-world benchmark comprising 19,500 real co-registered ground-to-space image pairs with real atmospheric PSF variation. Experiments demonstrate that FluxFlow consistently outperforms existing baseline methods in both photometric and scientific accuracy.

We study generative modeling of graphs with recurring subgraph motifs. We propose Flowette, a continuous flow matching framework that employs a graph neural network-based transformer to learn a velocity field over graph representations with node and edge attributes. Our model promotes topology-aware alignment through optimal transport-based coupling and encourages global structural coherence through regularisation. To incorporate domain-driven structural priors, we introduce graphettes, a new probabilistic family of graph structure models that generalize graphons via controlled structural edits for motifs such as rings, stars, and trees. We theoretically analyze the coupling, invariance, and structural properties of the framework, evaluate it on synthetic and molecular benchmarks, and isolate the contributions of the structural prior, the optimal-transport coupling, and the regularisation terms through controlled ablations. Flowette achieves competitive performance overall, attaining state-of-the-art results on several metrics across multiple benchmarks, highlighting the effectiveness of combining structural priors with flow-based training for modeling complex graph distributions.

Battery degradation remains a central challenge in the development and broad application of sustainable energy technologies. Accurate degradation prediction is challenging, as battery aging emerges from complex and heterogeneous interactions among cycling behavior, operating conditions, and cell chemistry. Existing machine-learning approaches typically focus on deterministic end-of-life predictions or modeling degradation curves within fixed chemistry settings, leaving probabilistic state-of-health (SOH) trajectory modeling across heterogeneous chemistries underexplored. We introduce FlowBatt, a use-inspired conditional generative framework that adapts flow matching with a diffusion transformer (DiT) backbone to battery degradation trajectory modeling. FlowBatt models full SOH trajectories as probabilistic degradation processes conditioned on early-cycle capacity data. To strengthen this conditioning pathway, we use explainable AI analysis to diagnose and improve the encoder that maps early-cycle capacity matrices into conditioning vectors. We evaluate FlowBatt on five public benchmark settings spanning diverse chemistries and aging conditions, comparing it with supervised and diffusion-based trajectory models as well as established baselines for remaining-useful-life (RUL) prediction under shared data splits. FlowBatt achieves the best SOH prediction performance on four of five datasets, with errors below 2.5%, and delivers competitive RUL prediction performance. By generating multiple plausible trajectories, FlowBatt provides empirical uncertainty estimates, while also revealing calibration challenges under some dataset shifts. These results indicate that flow-matching-based trajectory modeling is a promising framework for probabilistic battery health prediction.