NeurIPS 2026 Papers

Discrete diffusion language models (DLMs) enable parallel generation but usually rely on fixed forward processes, such as masking, uniform noise, or precomputed hierarchies. We investigate whether the hierarchical forward process can instead be learned while preserving continuous-time tractability. We propose \textbf{Learnable Hierarchical Diffusion Language Model (LHDLM)}, which extends a learnable column-stochastic token-cluster map. This many-to-many hierarchy preserves a CTMC with block-conditional transition and closed-form CT-ELBO, while recovering HDLM in the one-hot limit and masked diffusion in the collapsed limit. We identify degenerate hierarchy maps caused by learning the same map used in both forward targets and model-induced cluster predictions, and mitigate them with an information-retention regularizer. Empirically, LHDLM is competitive with discrete diffusion approaches and reveals soft token structures --- cluster-agnostic function tokens and sharp content-token assignments --- that cannot be represented by hard partitions.

Diffusion models have recently emerged as a powerful paradigm for generating 3D molecules. Despite showing remarkable promise, they learn atomic distributions implicitly from data, without explicitly encoding physicochemical rules into their generative dynamics. Consequently, generated samples can be statistically plausible yet chemically invalid. To address this problem, we propose Sequential Neuro-Symbolic Constrained Diffusion (SensDiff), a framework that integrates symbolic rules into generative modeling, enabling the model to internalize scientific priors during training. Central to SensDiff is the observation that the diffusion trajectory of 3D molecule generation exhibits a coarse-to-fine evolution: valid molecules arise by first mitigating macroscopic geometric conflicts and then refining structures toward microscopic chemical consistency through iterative denoising. Accordingly, SensDiff mirrors this dynamic by sequentially enforcing constraints with adaptive weighting during training, progressively steering generation toward valid molecular geometries. Moreover, SensDiff translates domain knowledge into interpretable generative controls, grounding opaque neural denoising in scientific principles. Experiments on molecular benchmarks and real-world constrained generation tasks confirm that SensDiff consistently improves chemical validity while adhering to physicochemical rules and user-specified targets.

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

Large distribution shifts remain a primary obstacle for domain generalization and unsupervised adaptation. Although gradual domain adaptation alleviates this difficulty by introducing ordered intermediate domains, most existing approaches still operate in a discrete, step-wise manner, which can accumulate errors and often relies on unstable Min--Max optimization. We propose \textbf{FlowGDA}, a flow-matching framework that models gradual adaptation as \emph{continuous} transport on a statistical manifold in a representation space. FlowGDA learns time-dependent velocity fields that induce smooth domain trajectories, using a simulation-free regression objective rather than adversarial training. To prevent semantic drift, we couple left-to-right transport between consecutive domains with a source-anchored transport and a semantic consistency loss, and we further stabilize learning via a two-stage sequential optimization scheme. Extensive experiments demonstrate that our method outperforms state-of-the-art techniques, validating flow matching as an effective alternative for domain adaptation.

Current text-to-image diffusion models remain unreliable for culturally grounded generation, often producing incorrect or stereotyped depictions, particularly for underrepresented cultures. While prior work has largely focused on evaluation and benchmarking, improving cultural generation remains underexplored. In this work, we study cross-cultural image generation through cultural vectors, defined as the difference between fine-tuned and pretrained model parameters. We show that cultural vectors enable fine-grained control over cultural alignment and failure modes through simple scaling at inference time. We further find that deeper U-Net layers encode stronger cultural information, while cultural vectors across countries occupy largely independent directions in parameter space. However, unlike prior work on task arithmetic, naively combining cultural vectors fails to produce meaningful multi-cultural behavior due to strong interference across cultures. Motivated by this limitation, we propose Descriptor-Guided Merging (DGM), a culturally-aware merging approach that estimates cultural vectors for unseen countries using descriptor-based similarities across cultures. Experiments on two benchmarks across 16/10 countries show that cultural vectors improve generation over pretrained models by 18.9%, while DGM improves cross-cultural generalization by 4.2% over naive merging.

Generative models, from diffusion models to large language models, achieve remarkable performance but at a cost in training data orders of magnitude larger than what biological learners require. An alternative paradigm has emerged in which networks are trained to predict their \emph{own} latent representations of related views or masked regions, as in data2vec and JEPA -- an idea related to predictive-coding accounts of the cortex. Despite strong empirical results, the theoretical understanding of these methods remains limited. Central questions include: by how much does latent prediction actually improve data efficiency? Is there a benefit to stacking such methods into multi-scale hierarchies? We answer both using as data a tractable probabilistic context-free grammar that captures the compositional structure of natural language and images. We prove that latent prediction recovers the full latent tree of depth $L$ from a number of samples scaling as $m^3$, where $m$ is the number of production rules per symbol. This is much fewer than the $m^L$ samples required by supervised learning and the $m^{L+1}$ required by token-level SSL. We confirm this bound with (i) a hierarchical clustering algorithm, (ii) an end-to-end neural network whose predictor-clusterer modules predict their own latents at each level via gradient descent, and (iii) the first sample-complexity analysis of data2vec, which we show implicitly performs hierarchical latent prediction. This suggests that explicit stacking such as H-JEPA is largely redundant.

Masked diffusion models (MDMs) have emerged as a promising alternative to autoregressive models, enabling parallel token generation while achieving competitive performance. Despite these advantages, MDMs face a fundamental limitation: once tokens are unmasked, they remain fixed, leading to error accumulation and ultimately degrading sample quality. We address this by proposing a framework that trains a model to perform both unmasking and correction. By reusing outputs from the MDM denoising network as inputs for corrector training, we train a model to recover from potential mistakes. During generation we apply additional corrective refinement steps between unmasking ones in order to change decoded tokens and improve outputs. We name our training and sampling method **Pro**gressive **Se**lf-**Co**rrection (**ProSeCo**) for its unique ability to iteratively refine an entire sequence, including already generated tokens. We conduct extensive experimental validation across multiple conditional and unconditional tasks, demonstrating that \method~yields better quality-efficiency trade-offs (up to ~4x faster sampling) and enables inference-time compute scaling to further increase sample quality beyond standard MDMs (up to ~1.2x improvement on benchmarks).

Transcriptome-conditioned whole-slide image (WSI) synthesis aims to decode the complex mapping from molecular states to histologic phenotypes. Existing generative paradigms predominantly rely on a direct black-box transcriptome-to-image mapping, tasking a single generator with the simultaneous interpretation of transcriptome signals, inference of multicellular spatial organization, and rendering of fine-grained textures. This formulation, however, is structurally under-constrained; the underlying tissue architecture, the critical substrate linking gene expression to morphology, remains latent and only weakly supervised by pixel-level objectives. We present \textsc{TopoScape}, a topology-anchored framework for transcriptome-to-histology generation under a \emph{Layout-Before-Pixels} principle. Instead of synthesizing pixels directly from transcriptomic embeddings, \textsc{TopoScape} first resolves molecular states into explicit, multi-class cellular topologies via an RNA-guided Topological Prior Generator, reinforced by persistence-based topological regularization. These resolved topologies are further reparameterized into a suite of topology-derived controls, including structure-aware initialization, continuous density fields, and distance representations, which guide a hierarchical, frequency-decoupled flow-matching trajectory. By introducing multicellular organization as an explicit structural mediator, \textsc{TopoScape} allows molecular states to deterministically shape both the macroscopic tissue architecture and the microscopic generative process. Across five TCGA benchmarks, \textsc{TopoScape} consistently outperforms state-of-the-art methods in generative fidelity, biological realism, and downstream predictive utility. Code and pretrained models will be released.

Geometric foundation models, such as the Visual Geometry Grounded Transformer (VGGT), provide strong 3D priors from unposed images. However, such models operate purely in a feed-forward, deterministic regime, \ie~they cannot generate plausible geometry beyond what the input views directly support. Generative models for 3D scenes, on the other hand, must rely on strong geometric priors to produce coherent outputs from sparse inputs. We bridge these two paradigms by performing flow matching directly in VGGT's latent space, leveraging its learned 3D priors without committing to any explicit downstream representation such as Gaussians, meshes, or video-VAE latents. This requires respecting the latent geometry: VGGT tokens occupy a product of high-dimensional hyperspheres on which standard Euclidean flow matching fails. We address this with a Riemannian Flow Matching framework defined on a product manifold of four hyperspheres, aligned with VGGT's multi-scale encoder, which keeps generated tokens on the valid data manifold required by the frozen decoding heads. On RealEstate10K and ScanNet++, our method achieves strong performance against recent scene generation baselines in both per-view 3D geometry and appearance, establishing latent-space flow matching on geometric foundation models as a viable paradigm for 3D generation.

Autoregressive (AR) models remain the dominant paradigm for natural language generation, but their strictly sequential decoding process leads to high inference latency. Recent diffusion-inspired language models, such as LLaDA and Dream, alleviate this issue through parallel generation, yet they still face two key limitations: information loss, since predictive distributions over non-finalised tokens are discarded at each step, and unstable commitment dynamics, where local token decisions are not sufficiently coordinated at the global level. We propose Latent Refinement Decoding (LRD), a two-stage decoding framework consisting of Latent Refinement and a Predictive Feedback Loop. In the first stage, LRD keeps masked positions as distributional mixtures of predicted tokens and the mask embedding, enabling the model to form more globally consistent beliefs before committing tokens. In the second stage, LRD progressively finalises confident tokens while preserving uncertain ones for further iterative refinement, with KL-divergence dynamics serving as a stable criterion for convergence and early stopping. Experiments show that LRD improves performance on both coding tasks, including HumanEval by 6.3 and MBPP by 2.6, and reasoning tasks, including GSM8K by 2.9 and MATH500 by 3.8, while achieving up to 10.6× overall speedup. Moreover, LRD is compatible with single-token decoding, multi-token threshold commitment, and system-level accelerators; when combined with Fast-dLLM, it reaches up to 18.4× speedup over vanilla decoding while further improving accuracy.

Many recent flow-matching and diffusion-style generative models rely on auxiliary stochastic dynamics during training: a richer process is simulated to define conditional targets, but the auxiliary state is either intractable to sample at generation time or simply not part of the desired output. Existing Generator Matching theory formalises conditioning on static latent random variables, and several recent papers prove special cases of projection results for particular augmented-state constructions. We introduce latent process generator matching, a general framework that treats the observed generative state as a deterministic image $X_t=\Phi(Y_t)$ of a tractable Markov process $Y_t$. We show that in this setting one may learn the generator of a stochastic process on the image space which has the same one-time marginal distributions as the projected process. This generalizes and subsumes the discrete latent process results from the literature, and extends Generator Matching from static latent variables to a rich family of time-dependent latent conditional processes.

Video diffusion models often fail in precisely the dimension that distinguishes videos from images: motion. Standard reconstruction and flow-matching objectives in pixel or VAE-latent space are dominated by appearance, so visually similar clips can be treated as close even when their underlying dynamics differ. We propose Latent Motion Alignment, a training-time objective that compares predicted and ground-truth videos in a learned motion space. This space is learned by training a compact encoder to describe how one latent frame changes into the next, while a decoder ensures that the resulting token captures information needed to model the transition. Once learned, the encoder is frozen and used as an auxiliary loss for fine-tuning video diffusion models. The motion module is used only during training and adds no inference-time cost. We validate that the learned space separates motion rather than appearance shortcuts, improves motion-sensitive generation metrics, and enables fine-grained Olympic-diving generation where jump type and score depend on subtle temporal structure.

Reliable physics simulation requires both broad generalization across heterogeneous PDE families and stability under long autoregressive rollouts. Current neural solvers rarely provide both. Deterministic operators accumulate rollout error, while probabilistic solvers typically remain tied to a single PDE family or a short prediction horizon. We address this gap with the \textbf{Latent Generative Solver} (LGS), which couples a Physics VAE (PhyVAE) with a Pyramidal Flow-Forcing Transformer (PFlowFT). PhyVAE compresses states from twelve PDE families into a shared \emph{physical manifold}, separating dynamics-relevant structure from the ambient state space. PFlowFT then predicts the next latent state through input-noised flow matching, yielding a sufficient-condition contraction mechanism that explains improved autoregressive rollout stability. Pretrained on a 2.5\,M-trajectory, 16-system corpus at $128^2$ resolution, LGS obtains the lowest relative $L_2$ error (L2RE) on 15 of 16 systems at both 5- and 10-step rollout. At 20 steps, LGS reduces the L2RE from $56.1\%$ to $\mathbf{30.2\%}$ against matched deterministic and adapted generative baselines, while requiring $\mathbf{13}$--$\mathbf{77\times}$ less recurrent dynamics-step compute. On a held-out $256^2$ Kolmogorov flow, LGS reduces the 1-step L2RE from $0.398$ to $0.129$ within five finetuning epochs; U-AFNO achieves only $0.653$ to $0.343$ under the same protocol.

Transformers update token representations through multi-head attention and residual connections as $X \leftarrow X + \sum_{i} P^{(i)}XW_{V_i}W_{o_i}$, where $P^{(i)}$ is the softmax attention matrix in head $i$. We propose replacing a subset of $P^{(i)}$'s with the Laplacian $I - P^{(i)}$, giving $X \leftarrow X + \sum_{i \in \mathcal{A}} P^{(i)}XW_{V_i}W_{o_i} + \sum_{i \in \mathcal{L}} (I - P^{(i)})XW_{V_i}W_{o_i}$. Our proposal has two motivations. First, it allows attention heads to update the mean of token representations, while Laplacian heads can directly control within-sequence variance. Second, if tokens are viewed as nodes in a graph with edge weights \(P^{(i)}\), then \(I - P^{(i)}\) is the corresponding graph Laplacian, and the update can be interpreted as one step of heat diffusion on the graph. We show that this simple modification improves performance across supervised learning, language modeling, and self-supervised learning tasks. To investigate why, we examine the token representations learned with and without Laplacian heads. In supervised learning, Laplacian heads collapse token representations within the same sequence and align the sequence means with the geometry of Neural Collapse. In language modeling, they increase the separability of token representations that share the same next-token prediction. In self-supervised learning, they produce token representations whose principal components are better suited for segmentation. Across modalities, they also lead to faster-decaying spectra, indicating stronger token smoothing. Overall, our findings challenge the prevailing view that token oversmoothing is inherently harmful, showing instead that certain forms of smoothing can be beneficial.

Continuous diffusion has served as a foundation for high-fidelity, controllable, and few-step generation across continuous data modalities such as images, videos, and molecular structures. However, in language modeling, prior continuous diffusion language models (DLMs) lag behind discrete counterparts. Existing categorical and simplex-based approaches operate over extremely large and sparse language spaces, while prior embedding-space approaches avoid this sparsity but lack a well-selected design space. In this work, we close this gap with **LangFlow** by connecting embedding-space DLMs to Flow Matching, alongside three key innovations: (1) we derive a novel ODE-based NLL bound for principled evaluation of continuous flow-based language models; (2) we propose an information-uniform principle for setting the noise schedule, which motivates a learnable noise scheduler based on a Gumbel distribution; and (3) we revise prior training protocols by incorporating self-conditioning, which improves both likelihood and sample quality for embedding-space DLMs and behaves differently from its use in discrete diffusion. Putting everything together, LangFlow is competitive with top discrete DLMs on both perplexity (PPL) and generative perplexity (Gen. PPL), reaching a PPL of **30.0** on LM1B and **24.6** on OpenWebText. It also exceeds autoregressive baselines in zero-shot transfer on 4 out of 7 benchmarks. As the first continuous DLM shown to rival discrete diffusion in both generative quality and perplexity, LangFlow provides clear evidence that continuous diffusion is a promising paradigm for language modeling. Code will be released upon acceptance.

Sign Language Video Generation (SLVG) aims to generate realistic and motion-accurate sign language videos from spoken text. Most existing studies heavily rely on intermediate representations (\eg poses or 3D meshes), and adopt a two-stage generation paradigm, where the text is first converted into poses or other visual modalities, which are then used as conditions to synthesize sign language video frames via diffusion models (\eg pose-to-image models). However, the end-to-end SLVG task remains largely unexplored. In this paper, we demonstrate that end-to-end SLVG is feasible without relying on intermediate representations(\eg poses), and we argue that a key challenge lies in how to generate effective and temporally consistent conditions. With well-designed condition modules, it becomes feasible to build an end-to-end SLVG model without relying on any intermediate modalities. To this end, we propose LLMCond, a first end-to-end text-to-video SLVG framework that requires no auxiliary visual cues during either training or inference. LLMCond consists of four key components: (1) a video VQVAE that compresses sign language videos into a sequence of discrete latent tokens; (2) \textbf{an LLM-based conditioner} that generates temporally and semantically aligned conditions corresponding to the sign sequences; (3) \textbf{a Gaussian Condition Refiner} designed to enforce temporal smoothness across conditions, enabling the generation of coherent and natural sign language motions; and (4) a discrete diffusion model that synthesizes motion-accurate sign language videos conditioned on the refined condition sequences. Extensive experiments on public SL datasets demonstrate that LLMCond achieves highly competitive performance, producing temporally coherent and accurate sign language motions without relying on auxiliary visual modalities such as pose, depth, or optical flow.

Distilled diffusion models accelerate image generation by reducing the number of denoising steps, but often suffer from degraded image quality. To mitigate this trade-off, test-time optimization methods improve quality, yet their iterative nature incurs substantial computational overhead and leads to slow inference, limiting practical usability. Recent hypernetwork-based approaches amortize this process during training, but still require costly noise modulation in high-dimensional latent spaces. In this work, we propose LENS (Low-frequency Eigen Noise Shaping), an efficient noise modulation framework that operates in a low-dimensional subspace. Our approach is motivated by the observation that low-frequency components of the noise largely determine the global structure and visual fidelity of generated images. Based on this observation, we provide a theoretical justification for restricting modulation to the low-frequency subspace and derive a principled training objective. Building on this, LENS employs a lightweight, standalone network to selectively modulate these components, enabling efficient and targeted noise modulation. Extensive experiments demonstrate that LENS achieves competitive image quality while reducing FLOPs by 400–700$\times$, model parameters by 25–75$\times$, and inference-time overhead by 10–20$\times$ compared to prior methods.

Object detection data contains a structural asymmetry that is easy to overlook in dataset distillation (DD). Each detection image couples a spatial layout with a visual realization. Layouts define detection targets through object categories and bounding boxes, while pixels instantiate these targets with particular object appearances and backgrounds. Although both forms can be redundant across a dataset, they play different roles. Layouts define the task distribution, so synthesizing them freely risks altering the detection problem. Visual realizations, on the other hand, are conditional samples attached to layouts. This motivates a separation principle: preserve and recombine layouts from the original data, then use generative priors to diversify their visual realizations. Based on this principle, we propose LCD$^3$, a layout-conditioned diffusion framework for object detection DD. LCD$^3$ constructs composite layouts from diverse groups based on scene-level embeddings. A layout-conditioned diffusion model then generates new images from these layouts, enriching object appearance and scene realization without discarding the spatial structure needed for detection. The generation process is grounded with semantically verified object crops to retain the original visual style. Experiments show that this separation between layout and realization produces more effective distilled detection datasets. LCD$^3$ consistently outperforms the previous state-of-the-art, OD$^3$, across benchmarks using fewer objects per distilled image, e.g., a $12.5$\% mAP50 improvement at a $0.5$\% compression ratio on PASCAL VOC.

Learning high-quality latent actions from large-scale unlabeled videos, coupled with limited real-world interaction data for training an action decoder, has emerged as a promising paradigm for scalable latent policy learning. However, existing approaches typically rely on behavior cloning, which tends to collapse inherently multimodal action distributions into unimodal ones, thereby degrading the pretrained latent action structure. While flow matching provides a potential alternative, directly applying it leads to a misalignment between latent actions and physical actions during action decoder training, due to the stochastic nature of the learned policy. To address these, we propose Latent Action Flow Policy (LAFP), which leverages flow matching for latent policy learning and introduces an inference-time interpolation mechanism to mitigate stochasticity-induced misalignment. Experimental results demonstrate that LAFP consistently outperforms prior methods on downstream imitation learning tasks, achieving up to 10–15\% improvement in success rate while incurring less than 1× additional inference overhead.