NeurIPS 2026 Papers

Speech is an increasingly promising biomarker for neurodegenerative disorders due to its non-invasive nature, low cost, and suitability for frequent, longitudinal monitoring. However, existing clinical speech datasets are typically small, sparse, and irregularly sampled, limiting the ability to model continuous disease progression and develop robust biomarkers. We propose L-Flow, a progression-aware conditional speech generation framework for longitudinal speech trajectory completion. Given a patient’s speech recordings, timestamps, and clinical progression labels, L-Flow learns a query-specific progression representation to synthesize speech at intermediate time points within the observed recording span. Experiments on two real-world longitudinal speech datasets demonstrate that L-Flow generates synthetic speech with stronger progression consistency than eight baseline augmentation methods. In addition, incorporating L-Flow–augmented data improves downstream regression performance to predict clinical severity, highlighting its utility for speech-based biomarker development.

Probabilistic time-series forecasting requires models that simultaneously capture structured temporal dynamics, expressive uncertainty, and efficient inference, yet existing approaches fall short of this goal: latent dynamical models impose structure but rely on restrictive generation mechanisms, while modern generative methods such as diffusion and flow matching achieve flexibility at the cost of iterative and computationally expensive sampling. We introduce the Koopman Generative Operator (KGO), a probabilistic forecasting method that conceptualizes prediction as the evolution of structured uncertainty. KGO integrates three core components: (1) Koopman Patch Embedding (KoPE) for temporally consistent latent trajectory extrapolation; (2) Koopman Flow Matching (KoFM), which enables fast, single-step generation through a closed-form matrix exponential in a Koopman latent space, bypassing iterative sampling; and (3) an Adaptive Uncertainty Gate (AUG), which provides calibrated predictions by adapting uncertainty per-variable and per-horizon, corresponding to a learned decomposition of aleatoric uncertainty without manual tuning. By unifying these components, KGO achieves state-of-the-art accuracy across the majority of ProbTS datasets, outperforming existing methods on 12/17 benchmarks in CRPS and 11/17 in NMAE. Further, by eliminating iterative sampling, KGO delivers at least a 25$\times$ reduction in inference time compared to iterative generative models. These results establish KGO as a practical, principled, and highly scalable framework for next-generation probabilistic forecasting.

Metric-induced discrete flow matching (MI-DFM) exploits token-latent geometry for discrete generation, but its practical use is limited by two issues: heuristic schedulers requiring hyperparameter search, and finite-step path-tracking error from its first-order continuous-time Markov chain (CTMC) solver. We address both issues. First, we derive a kinetic-optimal scheduler for prescribed scalar-parameterized probability paths, and instantiate it for MI-DFM as a training-free numerical schedule that traverses the path at constant Fisher–Rao speed. Second, we introduce a finite-step moment correction that adjusts the jump probability while preserving the CTMC jump destination distribution. We validate the resulting method, GibbsTTS, on codec-based zero-shot text-to-speech (TTS). Under controlled comparisons with a unified architecture and large-scale dataset, GibbsTTS achieves the best objective naturalness and is preferred in subjective evaluations over masked discrete generative baselines. Additionally, in comparison with the evaluated state-of-the-art TTS systems, GibbsTTS shows strong speaker similarity, achieving the highest similarity on three of four test sets and ranking second on the fourth. Demo and code are available in the supplementary materials.

We propose kernel-gradient drifting, a one-step generative modeling framework that replaces the fixed Euclidean displacement direction in drifting models with directions induced by the kernel itself. Standard drifting is attractive because it enables fast, high-quality generation without distilling a large pretrained diffusion model, but its theory is currently understood mainly for Gaussian kernels, where the drift coincides with smoothed score matching and is identifiable. Our gradient-based reformulation exposes this score-based structure for general kernels: the resulting drift is the score difference between kernel-smoothed data and model distributions, yielding identifiability for characteristic kernels and a smoothed-KL descent interpretation of the drifting dynamics. Since kernel gradients are intrinsic tangent vectors, the same construction extends naturally to Riemannian manifolds and to discrete data via the Fisher-Rao geometry of the probability simplex. Across spherical geospatial data, promoter DNA and molecule generation, kernel-gradient drifting enables state-of-the-art one-step generation beyond the Euclidean setting without distillation.

Training-free safeguards for text-to-image diffusion models often rely on a reusable safety signal, such as an unsafe direction or global toxic subspace, applied broadly across prompts. We provide a controlled geometric analysis of this global-unsafety assumption and reveal a consistent coverage-selectivity trade-off: compact unsafe subspaces fail to cover heterogeneous unsafe semantics, whereas broader aggregation increasingly distorts safety-adjacent benign prompts. Motivated by this finding, we propose CALM (Counterfactual Adaptive Local Modulation), a training-free safeguard that replaces uniform global removal with prompt-local counterfactual correction. Using matched unsafe-benign anchors, CALM routes each prompt to active unsafe categories, minimally edits only violating token representations toward the safe side, and suppresses positively aligned unsafe residual components. Across broad evaluation, CALM improves unsafe-content suppression while preserving benign utility, demonstrating that local counterfactual correction provides a more selective alternative to global unsafe-signal removal.

Reconstructing the connectome of the brain is a central goal of modern neuroscience, but the required electron microscopy (EM) imaging is extremely time-consuming. EM image super-resolution (SR) accelerates this acquisition for downstream neuron segmentation, yet existing methods do not adequately couple SR with segmentation for EM: SR lacks segmentation guidance, and segmentation cannot adapt to super-resolved features. In this work, we propose a joint SR and segmentation framework specifically designed for EM images. In the super-resolution part, we introduce segmentation as an auxiliary task via a shared encoder with task-specific decoders to provide a semantic prior, improving reconstruction fidelity. In the segmentation part, we introduce a lightweight partial diffusion model that initializes denoising from a partially noised SR embedding, producing a structural prior that closely approximates real HR features and enhances segmentation accuracy on super-resolved EM images. Extensive experiments across multiple datasets and degradation settings demonstrate the superior performance of our framework.

Local intrinsic dimension (LID) quantifies the degrees of freedom of the data manifold around a point and is widely used to detect memorization, diagnose distribution shift, and characterize learned representations. Existing generative-model-based LID estimators are model-specific: they rely on a score, a log-density Hessian, or an exact log-likelihood, and therefore do not apply to ODE-based generators (flow matching, rectified flows, stochastic interpolants, and CNFs) that expose only a velocity field. We propose JaSpec, a model-agnostic LID estimator that counts the singular values of the velocity-field Jacobian $J_t = \partial f_\theta / \partial x$ that fall below a threshold $\tau$. JaSpec applies uniformly to score-based diffusion (via the probability-flow ODE) and to flow-based generators, and recovers Hessian-based estimators on probability-flow diffusion as a verification special case. We prove a direct dynamical identifiability theorem under a Jacobian-normal-dominance condition stated entirely in terms of $J_t$ and verified by an empirical spectral-gap diagnostic. On VP-SDE diffusion and OT-CFM flow-matching benchmarks with known LID, JaSpec attains MAE $= 0$ on most settings up to $D{=}3072$, where no prior model-based estimator reaches zero error, and improves over the strongest model-based baseline by an order of magnitude on the hardest $3072$-dimensional nonlinear mixture. We provide both an exact $\mathcal{O}(D^3)$ path and a linear-cost stochastic Lanczos quadrature path. JaSpec is, to our knowledge, the first LID estimator applicable to flow matching, rectified flows, and generic differentiable ODE generators.

Neural responses to the same stimulus can vary dramatically with fluctuations in the brain's internal state and the organism's behavioral state. Yet studying how brain state shapes neural responses is difficult: limited experimental recordings sparsely sample this joint space, leaving many biologically valid state-stimulus pairings unobserved. Existing methods either capture state-dependent modulation with restricted model assumptions or synthesize neural activity without explicitly controlling internal brain state. We introduce **BrainStateDiff**, a conditional diffusion framework that models the spatiotemporal distribution of future neural activity and behavior given external stimuli and recent brain states. Motivated by two gaps in finite recordings, missing state-stimulus combinations and limited repeats of observed conditions, BrainStateDiff introduces two state-aware sampling strategies: *cross-state sampling*, which recombines observed states and stimuli to synthesize plausible neural responses from unobserved pairings, and *matched-state sampling*, which resamples from observed pairings to capture local trial-to-trial variability. We evaluate BrainStateDiff on our newly collected wide-field calcium imaging data in mouse V1, electrophysiology data in monkey V4, and two-photon calcium imaging data in mouse striatum. Our results show that BrainStateDiff generates biologically meaningful samples that preserve the state-dependent structure of real recordings and expand neural response space coverage beyond the original recordings. BrainStateDiff establishes state-conditioned generative modeling as a practical framework for studying how internal brain state shapes neural responses beyond the state-stimulus combinations directly observed in the experiments.

Flow Matching (FM) provides an efficient formulation for continuous-time generative modeling via straight optimal transport (OT) trajectories. However, during accelerated sampling, these models face a fundamental variance-fidelity dilemma. Under few-step deterministic Ordinary Differential Equation (ODE) integration, the rigid OT trajectories suffer from mean concentration, leading to severe variance collapse and the loss of high-frequency details. Conversely, traditional Stochastic Differential Equations (SDEs) inject blind, exogenous Brownian noise to recover variance, but this isotropic exploration incurs inherent numerical attrition over long integration paths, bottlenecking peak fidelity. To resolve this, we introduce Self-Aligned Drifting (SADrift) to mitigate these challenges without external priors. SADrift is an inference-time framework that augments flow matching inference with self-interacting dynamics, without additional training. By maintaining a momentum history of the sampling trajectory, SADrift extracts the \emph{kinematic residual} to generate a deterministic extrapolative field. This mechanism forces the trajectory to efficiently explore the local tangent space, effectively decoupling exploratory variance into targeted deterministic dispersion and a minimal stochastic buffer. To safely anchor these dispersed trajectories and prevent out-of-distribution divergence, the residual drift is analytically integrated into a micro-time Ornstein-Uhlenbeck (OU) process, providing a mathematically sound, mean-reverting geometric safeguard. Requiring exactly zero additional Neural Function Evaluations (NFE), SADrift empowers a frozen base model to achieve a highly competitive FID of 2.00 at just 20 NFE on ImageNet-256. By successfully bypassing the numerical attrition of the 250-step SDE baseline (FID 2.06), SADrift establishes a new Pareto frontier for variance injection. Beyond image synthesis, we further validate SADrift on fast video generation paradigms (e.g., TurboDiffusion with Wan2.1-1.3B), demonstrating its universal capability to unlock latent generative quality across different modalities and acceleration regimes.

Diffusion-based generators set the current state of the art for synthetic tabular data, deployed downstream wherever direct access to real records is restricted. These methods approach but rarely exceed real-data utility on downstream tasks, and closing this synthetic--real performance gap has so far been pursued exclusively at training time, via architectural advances, scaling, and retraining of monolithic generators. The inference-time alternative, i.e., refining the outputs of a pre-trained backbone with parameters left untouched, has remained largely unexplored for tabular synthesis. We introduce $\textbf{TARDIS}$ (Tabular generation through Refinement, Distillation, and Inference-time Sampling), an inference-time refinement framework that operates on a frozen pre-trained backbone, configured per dataset by a Tree-structured Parzen Estimator search over score-level guidance during reverse diffusion, with each trial's objective set by an inner grid search over post-hoc sample selectors and an optional soft-label distillation step. The search space encodes a single mathematical pattern we name $\textit{Bidirectional Chamfer Refinement}$ (BCR): the symmetric Chamfer functional between synthetic and real samples is minimized both continuously, via a score-level gradient during reverse diffusion, and discretely, via batch-ranking post-generation. On the majority of datasets the search selects BCR-aligned configurations over alternatives encoded in the search space, evidence both for BCR as the dominant refinement pattern and for TARDIS's per-dataset search as a procedure that recovers this pattern. Across 15 binary, multiclass, and regression benchmarks TARDIS achieves a median $+8.6\%$ downstream-task improvement over models trained on real data (95\% CI $[+3.3, +16.4]$, Wilcoxon $p=0.016$, 11/15 strict wins) and improves over the underlying TabDiff backbone on all 15 datasets (mean $+12.9\%$, $p<10^{-4}$), matching the backbone on manifold fidelity, diversity, and sample-level privacy. The synthetic--real gap is therefore not primarily a training-time problem: on the studied corpus, inference-time refinement of a pre-trained tabular diffusion backbone reaches and exceeds real-data utility in 1 to 80 minutes on a single consumer-grade GPU.

Remote sensing imagery supports diverse visual tasks, such as object detection and semantic segmentation, but these tasks vary across scenes, imaging modalities, and target objects. Since many remote sensing scenarios lack sufficient annotations, conventional supervised learning is often difficult to apply, motivating in-context learning as a flexible alternative.We present an in-context learning framework for remote sensing visual tasks, where a new task is specified by a single annotated example and applied to unseen images without retraining at inference time. Built upon diffusion models, our framework establishes target-reference associations through cross-attention and transfers the structural relationship between the reference image and its annotation to produce task-specific predictions. Unlike natural images, remote sensing objects are often small and provide weak semantic cues in early diffusion steps, making semantic alignment between target and reference images difficult. We address this limitation with a semantic-aware cross-attention that combines semantic and fine-grained details for more accurate cross-image matching. Remote sensing objects also appear at arbitrary orientations, causing large appearance variations and unstable in-context transfer. To improve robustness, we introduce a rotation-robust learning strategy that reduces sensitivity to orientation changes. Experiments show that our method achieves strong one-shot performance, establishing a flexible paradigm for adapting remote sensing models to diverse visual tasks.

Generative models for function-valued data, such as time series and solutions to partial differential equations, must learn distributions over infinite-dimensional spaces rather than over finite-dimensional vectors. Functional Flow Matching (FFM) is a recent extension of Flow Matching to this setting, learning a velocity field whose flow transports a Gaussian prior to the data distribution. However, FFM inherits a structural limitation from standard Flow Matching: in each training batch, prior and data samples are paired independently, so the conditional bridge between them must simultaneously traverse the shared global structure of the dataset and instance-specific residuals. This limitation is more consequential in function space than in finite dimensions: directly formulating optimal transport on function spaces is technically delicate, and a flat Euclidean surrogate ignores the function-space geometry that distinguishes function-valued data. We propose kernel Functional Flow Matching (kFFM), which replaces the independent pairing by entropic optimal transport in a kernel-induced Hilbert space via the Hilbert Sinkhorn Divergence, leaving the FFM neural-operator architecture unchanged. Theoretically, we prove the HSD objective is well-posed on Banach ambient spaces with bounded kernels, derive compact-metric approximation bounds against quadratic-cost OT with an explicit kernel-cost mismatch term, and quantify the gap between the function-space objective and the truncated representation computed on a grid, at a rate governed by data regularity. Empirically, kFFM consistently improves MMD-RBF distributional matching over FFM, diffusion, adversarial, and finite-dimensional OT baselines on time-series and PDE benchmarks, with function-space-aware kernels emerging as the strongest choices on every PDE and path-valued benchmarks.

Diffusion-based posterior sampling (PS) is a leading framework for imaging inverse problems, combining learned priors with measurement constraints. Yet, its standard formulations rely on instantaneous data-consistent estimates, which induce temporal variability in the reverse dynamics. We reinterpret PS from a dynamical perspective, showing that the standard PS update corresponds to a first-order discretization of the diffusion dynamics plus a residual correction capturing the mismatch between the denoised prediction and the data-consistent estimate. A second-order discretization, however, naturally introduces a temporal correction based on the variation of consecutive estimates. Building on this, we propose LAMP, combining the second-order update with the residual correction characterizing a PS technique. LAMP thus inherits a lagged temporal correction, and it can be implemented as a modular plug-in over the PS backbone. We show that LAMP preserves the structure of a posterior sampler, and we perform a one-step risk analysis to characterize when LAMP improves the reverse transition via a bias-variance trade-off. Experiments across multiple imaging tasks demonstrate consistent improvements over strong baselines such as DiffPIR and DDRM, without increasing the number of denoising evaluations.

Feature caching accelerates Diffusion Transformers by reusing intermediate computations across denoising timesteps, yet existing methods share a fundamental blind spot: they treat the standard reference denoising trajectory as the optimisation target, approximating its per-step states and thus inheriting its output as an implicit quality ceiling. We argue that this target is arbitrary --- what truly matters is the ideal result, not the intermediate path taken to reach it. We propose IdealCache, a training-free framework that abandons step-wise imitation of the reference trajectory. Instead, it anchors caching on a per-input ensemble of ideal trajectories constructed from candidate target results, aggregates their geometry into a single graph, and discovers optimal non-uniform schedules via a constrained shortest path on this graph. By decoupling from the reference process, IdealCache breaks the performance bottleneck of trajectory-approximation; our schedules can attain near-lossless fidelity in generation and even surpass on task-specific metrics (e.g., maintaining higher semantic consistency in image editing). Without retraining, IdealCache achieves $6.35\times$ speedup on Qwen-Image, $5.84\times$ on Qwen-Image-Edit, and $4.32\times$ on HunyuanVideo, with competitive or superior quality across tasks.

Recent diffusion models have advanced image-conditioned video generation, but their accessibility raises risks of unauthorized manipulation. Image immunization has emerged as a promising defense for Image-to-Video (I2V) protection, yet existing methods often rely on degrading visual quality or temporal coherence. In this work, we revisit I2V immunization as reducing source-content preservation, shifting the focus from output degradation to weakening source-conditioned content propagation. To this end, we propose I2V-DETACH, an image immunization method that prevents unauthorized I2V generation through source grounding detachment. I2V models preserve source content by propagating source-image cues into video latents during denoising. Accordingly, I2V-DETACH disrupts this process in two complementary ways: it suppresses source-video grounding to reduce source cue propagation, and strengthens intra-video interactions to shift denoising toward video-side dynamics with reduced reliance on the source image. To obtain informative optimization signals, we initialize auxiliary video latents with source-oriented states that remain within the source-conditioned generation regime while deviating from source-preserving trajectories. Extensive experiments across diverse diffusion architectures show that I2V-DETACH substantially reduces source-content preservation, improves over prior immunization methods, and exhibits strong black-box transferability.

Hypergraphs capture high-order interactions that ordinary graphs cannot represent, yet generating realistic ones remains challenging because existing methods often rely on fixed structural assumptions or struggle to model coupled dependencies between nodes and hyperedges. In this work, we propose \textsc{Janus}, a latent diffusion framework that decomposes an observed hypergraph into sub-hypergraphs, learns coupled node and hyperedge latent representations with a dual-view $\beta$-VAE, and generates new structures through paired latent diffusion with cross-view conditioning. The method supports both unconstrained and node-set-constrained generation. We also introduce an evaluation protocol covering micro, meso, and macro scales interactions, structural reconstruction, and high-order similarity measures. Across five real-world datasets and nine baselines, \textsc{Janus} achieves the most stable performance across structural scales, with strong gains in meso-scale and high-order fidelity; in the constrained setting, it consistently obtains the best reconstruction results.

Hypergraphs model higher-order interactions, but realistic hypergraph generation remains difficult because incidence, hyperedge-size heterogeneity, and overlap structure are not faithfully captured by pairwise reductions. We propose HEDGE, a generative model defined directly on relaxed incidence matrices via a structured stochastic diffusion. The forward process combines a hypergraph-specific two-sided heat operator with an Ornstein--Uhlenbeck component, preserving structure-aware noising near the data while yielding an explicit Gaussian terminal law. Conditional on an observed hypergraph, this forward process is linear-Gaussian, so conditional means, covariances, scores, and reverse-drift targets are available in closed form. We therefore learn a permutation-equivariant state-only reverse-drift field in incidence space by regressing onto exact conditional targets, and generate samples by simulating a learned reverse-time SDE from the Gaussian base law. We establish exactness in the ideal state-only setting together with finite-horizon stability guarantees, and empirically show improved hypergraph generation quality relative to strong baselines.

Language-conditioned manipulation requires skill representations that are both multi-modal and predictable: the same instruction may admit diverse executions, while the high-level planner must select a stable skill for low-level control. However, vector-quantized skill codes compress continuous variations into isolated symbols, introduce biased straight-through gradients, and lack geometry for relating semantically similar skills. We propose $\textbf{HyperSkill}$, a hierarchical skill-learning framework that models skills as continuous embeddings on the unit hypersphere. We use a learnable von Mises--Fisher mixture prior to capture skill-level multi-modality, with geodesic repulsion encouraging diverse mode coverage on the hyperspherical manifold. To connect training-time skill inference with inference-time planning, we introduce Geodesic Skill Alignment (GSA), which aligns posterior skills inferred from demonstration segments with prior skills predicted by a high-level planner using squared geodesic distance. Together, these components provide a geometrically structured skill interface that preserves execution diversity while enabling causal skill prediction at inference time. For low-level control, a Conditional Flow Matching generator produces smooth, multi-modal action trajectories conditioned on skill embeddings. Experiments on LOReL and Kitchen demonstrate that HyperSkill achieves state-of-the-art success rates on the evaluated benchmarks. Ablation studies further validate the importance of each proposed component.

Diffusion-based visuomotor policies perform well in robotic manipulation, yet current methods still inherit image-generation-style decoders and multi-step sampling. We revisit this design from a frequency-domain perspective. Robot action trajectories are highly smooth, with most energy concentrated in a few low-frequency discrete cosine transform modes. Under this structure, we show that the error of the optimal denoiser is bounded by the low-frequency subspace dimension and residual high-frequency energy, implying that denoising error saturates after very few reverse steps. This also suggests that action denoising requires a much simpler denoising model than image generation. Motivated by this insight, we propose Hydra-DP3 (${\bf HDP3}$), a pocket-scale 3D diffusion policy with a lightweight Diffusion Mixer decoder that supports two-step DDIM inference. Our synthetic experiments validate the theory and support the sufficiency of two-step denoising. Futhermore, across RoboTwin2.0, Adroit, MetaWorld, and real-world tasks, HDP3 achieves state-of-the-art performance with fewer than 1\% of the parameters of prior 3D diffusion-based policies and substantially lower inference latency.