NeurIPS 2026 论文列表

Inference-time reward guidance is a simple way to improve generative models when completed outputs can be checked or scored by an external verifier. Best-of-N sampling is a particularly strong baseline: it is parallelizable and often highly improves with more samples. However, when the reference model assigns low probability to reward-satisfying samples, selection among independent full rollouts becomes sample-inefficient. We introduce MDM-VGB, a reward-guided discrete diffusion sampler that augments masked generation with value-guided re-masking. MDM-VGB extends the autoregressive VGB backtracking chain from fixed left-to-right prefix trees to any-order masked-state graphs, allowing the sampler to reveal and revise tokens at any position. The resulting Markov chain favors local reveal and re-mask moves that lead to higher-value partial masked states, enabling both root-start reward tilting and leaf-start editing of low-reward samples. We further introduce a flow-cancelled momentum lift of MDM-VGB that preserves the projected target law while reducing oscillatory reveal/re-mask dynamics under finite budgets. We prove that the sampler has the correct reward-tilted leaf law, places non-negligible stationary mass on complete outputs, and remains robust to partial-state verifier error. Across structured reward satisfaction and repair tasks, MDM-VGB improves the quality--cost frontier over reference sampling, best-of-N, and forward-only value-guided rollout.

Conditional Flow Matching (CFM) unifies conventional generative paradigms such as diffusion and flow-based models. Interaction Field Matching (IFM) is a recently proposed framework that generalizes Electrostatic Field Matching (EFM), rooted in Poisson Flow Generative Models (PFGM). While both frameworks define generative dynamics, they start from different objects: CFM specifies a conditional probability path in data space, whereas IFM specifies a physics-inspired interaction field in an augmented data space. This raises a basic question: **are CFM and IFM genuinely different, or are they two descriptions of the same underlying dynamics?** We show that they coincide for a natural subclass of IFM, which we call *forward-only* IFM. Specifically, we construct mappings between CFM and forward-only IFM and show that they induce the same generative dynamics. We further show that general IFM is strictly more expressive: it includes EFM and other interaction fields that cannot be realized within the standard CFM formulation. Our findings suggest developing generative models using both interpretations rather than treating them separately. Moreover, they highlight a novel direction for generative modeling based on backward-oriented field lines, which lies outside the conventional CFM formalism and may lead to new generative properties.

Generative models, such as diffusion and flow-based models, have emerged as powerful policy approximators in deep reinforcement learning (RL) due to their ability to represent multi-modal action distributions. However, their potential for maximum entropy RL remains largely untapped, as most existing methods treat generative processes as black-box samplers or rely on heuristic noise. In this paper, we propose GENIEO, a novel off-policy generative RL framework that leverages the exact intrinsic entropy of an augmented dummy-action policy to drive principled exploration. By designing a structurally invertible affine dual-variable flow, we bypass the numerical approximations of standard ODE solvers. This innovation allows us to rigorously apply the change-of-variables formula to derive a tractable and exact formulation for the augmented dummy-action policy entropy, enabling its direct integration into the off-policy learning objective. Experimental evaluations across 14 challenging tasks from the DMControl and HumanoidBench suites demonstrate that GENIEO achieves state-of-the-art (SOTA) performance. By effectively discovering optimal strategies in complex, high-dimensional environments, our approach bridges the gap between expressive generative modeling and maximum entropy RL.

We analyze generalization error, uniform stability, and uniform argument stability of gradient descent (GD) and stochastic gradient descent (SGD) over discrete parameter spaces, where each update involves deterministic or stochastic rounding. We show that deterministic rounding degrades the generalization error of GD on convex, Lipschitz, and smooth loss functions, increasing the rate from $O(T/n)$ to $O(T/\sqrt{n})$, and establish matching lower bounds. We further prove that uniform stability of GD becomes $\Omega(T)$, showing that stability-based generalization bounds are vacuous in this setting. In contrast, for the same losses, stochastic gradient descent with deterministic rounding admits nontrivial uniform stability guarantees, which differ qualitatively from the real-valued case and exhibit distinct dependencies on the number of iterations and the dimension: we prove tight bounds $O(T/n)$ for one dimension and $O(T^2/n)$ for higher dimensions. We also show that stochastic rounding can introduce generalization error that increases with the dimension; such a phenomenon is absent in standard real-valued optimization and in the deterministic rounding case. Finally, we provide upper bounds on uniform argument stability for stochastic rounding schemes and show that these bounds are tight when the loss can be represented as a sum of coordinate-wise functions.

Discrete diffusion models are typically trained by predicting the clean data given a noisy observation, which is then used with a certain choice of reverse transition parameterization. Two choices coexist in the literature, which we refer to as marginalization and plug-in. Although they coincide in the case of masked diffusion models (MDMs), we revisit this question for uniform diffusion models (UDMs), where the distinction matters. We show that the plug-in parameterization is not optimized by the denoising posterior but by a \emph{leave-one-out} posterior that removes the influence of the local observation. We give a thorough characterization of the resulting training target, together with exact conversion formulas between the denoiser, the \emph{leave-one-out} posterior, and the score. As a by-product, the leave-one-out characterization yields a Gibbs-based predictor–corrector scheme at no additional training cost. We further propose an absorbing-state construction of uniform diffusion, whose denoiser decomposes into simpler absorbing denoising posteriors, and which recovers the full UDM joint law following a simple resampling step. Empirically, we show that these design choices interact strongly with optimization and generative quality; on language modeling, the \emph{leave-one-out} denoiser improves over other parameterizations.

Understanding 4D scenes is a core challenge in visual intelligence, requiring models to jointly capture scene geometry, appearance, and dynamics from partial observations. Existing approaches, however, are subdivided into feedforward models that are used for direct geometric prediction and generative models for visual synthesis. We propose a unified generative-predictive framework for 4D scene understanding that jointly models RGB video and geometric representations such as depth and camera pose with a single joint generative model. Our generative formulation enables us to learn from diverse, heterogeneous datasets with different subsets of geometric and visual annotations, and enables us to condition on arbitrary subsets of inputs, allowing a single model to perform cross-modal generation, geometric prediction, and future scene inference from partial observations. In addition, our generative approach enables test-time search over multiple candidate scene completions, improving geometric prediction from sparse observations. Overall, we illustrate the efficacy of our generative-predictive framework on a suite of generation and prediction tasks.

Speculative decoding accelerates Large Language Models via draft-then-verify, where verification can be framed as an Optimal Transport (OT) problem. Existing approaches typically handle multi-draft and multi-step aspects in isolation, applying either flat OT to single-step drafts or per-token rejection sampling to tree-structured candidates. This separation leaves the joint regime (where multi-step dependencies meet multi-draft branching) poorly optimized, as local verification rules fail to exploit the coupling between horizontal and vertical dimensions of candidate trees. In this paper, we propose a unified perspective that casts tree-based verification as a conditional OT problem. Our key insight is that vertical dependencies can be abstracted through prefix acceptance probabilities, which act as dynamic scaling factors to actively guide horizontal draft selection. Based on this principle, we introduce UniVer, a verification algorithm that jointly optimizes across tree levels by composing local optimal transport plans under prefix constraints. We prove that UniVer remains lossless and achieves the optimal acceptance rate under the proposed conditional framework. Extensive experiments across different tasks and models demonstrate that UniVer improves acceptance length by 4.2\% to 8.5\% over standard recursive rejection sampling without replacement, while maintaining exact distributional alignment with the target model.

We investigate foundational questions about the interplay between memorization and learning in large language models (LLMs). When an LLM generates a string, can we disentangle the roles of rote memorization and contextual learning? Rote memorization results in an LLM regurgitating specific details of a training string, while contextual learning leads to the generation of new strings that follow generalizable patterns of the underlying language. Related questions of interest include: can an LLM avoid memorization when optimally learning a language?, and if not, can we design training schemes to reduce memorization and improve learning? To address these questions, we propose contextual memorization, a new measure that precisely disentangles memorization from learning. Using this measure, we establish that different training strings are memorized at different epochs in training, and that memorization of some training strings is unavoidable when optimally learning a language. Finally, we propose memorization-aware training, a scheme that dynamically down-samples training strings based on their memorization, and in doing so, equalizes learning across strings, reduces memorization, and improves learning. Our conclusions are supported by extensive experiments on multiple LLMs using formal languages as a controlled testbed, enabling precise language specification, exact string sampling, and elimination of data contamination; and further validated on natural languages.

Generative optimization uses large language models (LLMs) to iteratively improve artifacts (like code, workflows or prompts) using execution feedback. It is a promising approach to building self-improving agents, yet in practice remains brittle: despite active research, only 9% of surveyed agents used any automated optimization. We argue that this brittleness arises because, to set up a learning loop, an engineer must make "hidden" design choices: What can the optimizer edit and what learning evidence is provided per update? We investigate three factors that affect most applications: the starting artifact, batching execution traces as experiences, and determining a credit horizon with truncated traces. Through case studies in MLAgentBench, Atari, and BigBench Extra Hard, we find that decisions around these factors can determine whether generative optimization succeeds and they are not made explicit in prior works. Different starting artifacts determine which solutions are reachable in MLAgentBench, truncated traces can still improve Atari agents, and larger minibatches do not monotonically improve generalization on BBEH. We conclude that the lack of a simple, universal learning-loop setup across domains is a major hurdle for productionization and adoption, and provide practical guidance for making these design choices.

This position paper argues that understanding generalization in diffusion models requires fundamentally new theoretical frameworks that go beyond both classical statistical learning theory and the benign overfitting paradigm developed for supervised learning. In diffusion models, unlike in supervised learning, memorization of training data and generalization to novel samples are incompatible: a model that has fully memorized its training set generates copies rather than novel data. Several theoretical explanations for why practical diffusion models nevertheless generalize have been proposed, based on capacity limitations, implicit regularization from optimization, or architectural inductive biases, but their interactions remain unclear. We argue that the field should pivot from explaining why the diffusion models do not memorize to investigating what the models actually learn during pre-memorization phase. To highligh our stance, we conduct empirical study of diffusion models trained on CIFAR-10, and we distill the findings into concrete open questions that we believe are key to improve understanding of generalization in diffusion models.

The proliferation of multimodal data has underscored the imperative for efficiency in cross-modal retrieval. By mapping data into a unified Hamming space, Cross-modal hashing (CMH) significantly enhances both storage and computational efficiency, thereby establishing itself as a preferred favored paradigm for retrieval tasks. However most methods assume complete data, which rarely holds in practice. In incomplete settings, missing modalities (e.g., text or image) break semantic correspondence and make unsupervised hashing unreliable. Therefore, we propose Unsupervised Generative Completion and Graph-attention Refinement for Incomplete Cross-modal Hashing (UGGRH) method. Specifically, UGGRH leverages pretrained generative models for modality completion and employs a discriminator-guided similarity refinement module to fuse intra-modal relations with paired image-text matching signals, thereby constructing a robust cross-modal similarity matrix that yields a noise-tolerant similarity target for training. After that, it learns discriminative binary codes via hash-aware graph attention and cross-modal fusion, to refine modality embeddings and produce unified hash codes. Experiments on MIRFlickr25K, NUS-WIDE, and MS COCO datasets demonstrate that UGGRH consistently achieves superior performance under high missing rates and modality imbalance, showing significant improvements in retrieval accuracy and robustness across challenging incomplete scenarios.

Training loss and accuracy are the standard signals used to monitor generalization during deep neural network training. Two well-documented phenomena complicate this picture: in grokking, train loss falls rapidly while test performance improves abruptly only after a long delay; in epoch-wise double descent, train loss decreases monotonically while test loss or error rises and falls. Existing accounts are often task-specific, and a task-agnostic analysis framework for diagnosing and explaining these phenomena across realistic tasks and architectures is missing. We address this challenge by analyzing two competing processes that underlie learning dynamics: representation learning in the encoder and readout calibration in the final classifier. Using tools from representational geometry, neural tangent kernels, and linear probing, we show that both processes are active throughout training, with the fluctuations of their relative speed giving rise to seemingly anomalous generalization dynamics. Applying the representation-readout decomposition to grokking across a wide range of tasks and architectures, we find that the readout is train-biased before grokking onset, and representation learning is gradual but not absent—contrary to the lazy-to-rich account. The framework further provides diagnostic signatures distinguishing spurious from genuine generalization: in a previously reported MNIST grokking example and an epoch-wise double descent example, apparent delayed or non-monotone generalization is shown to arise from representation degradation and readout misalignment induced by non-standard training recipes. Together, these results establish the representation-readout decomposition as a top-down framework for understanding learning dynamics and revealing underlying algorithms for interpretability research.

Over the past few years, diffusion-based Schrödinger bridge models have been proposed to approximate optimal transport dynamics between two prescribed boundary distributions, with successful applications to generative modeling. More precisely, these methods aim to estimate a path measure whose initial and terminal marginals match the two boundary distributions, while minimizing the Kullback–Leibler divergence with respect to a reference Markov process. In this work, we consider the generalized Schrödinger bridge problem, in which the reference process is a twisted Brownian motion, that is, a Feynman–Kac transform of a Brownian motion induced by a time-dependent differentiable potential. Building on the Iterative Markovian Fitting (IMF) paradigm, and in particular on its special case Diffusion Schrödinger Bridge Matching (DSBM), which corresponds to the zero potential, we introduce Twisted Schrödinger Bridge Matching (TSBM), a diffusion-based method designed to handle both continuous- and discrete-time potentials. Unlike previous approaches, TSBM provides a rigorous extension of the IMF scheme to the generalized Schrödinger bridge problem. This derivation leads to a new bridge-matching loss that depends explicitly on the gradient of the potential and recovers the DSBM objective when the potential vanishes, yielding improved performance. We further introduce trajectory-based variance-reduction techniques that substantially stabilize optimization and may be useful beyond the present setting. Finally, we empirically demonstrate the benefits of TSBM on several experimental settings.

Latent generative models have emerged as powerful priors for solving inverse problems. These models typically represent a class of natural signals at a single, fixed complexity, governed by the latent dimensionality. This can be limiting: depending on the problem, a latent dimensionality that is too small may result in high representation error, while one that is too large may overfit to noise. We develop tunable latent priors for diffusion models, normalizing flows, and variational autoencoders, leveraging nested dropout. Across tasks including compressed sensing, inpainting, denoising, and phase retrieval, we show empirically that tunable priors consistently achieve lower reconstruction errors than fixed-complexity baselines. In the linear denoising setting, we derive the optimal complexity in closed form, showing how it depends on the noise level and the signal spectrum. This work demonstrates the potential of tunable latent generative priors and motivates both the development of supporting theory and their application across a wide range of inverse problems.

Many problems in diverse fields involve data that naturally live on Lie groups. However, existing Riemannian and Lie group generative models still face several limitations. Riemannian flow and consistency models often require position-dependent vector fields, and expensive geometric terms such as Euler-Arnold simulation on general Lie groups or covariant derivatives. Existing Lie group flow models are usually tied to collinear exponential paths, while momentum-based Lie group diffusion relies on compactness assumptions and does not naturally extend to non-compact groups. To address these limitations, we propose Trivialized Generative Models (TGM), a family of generative models that learns endpoint-constrained paths in the fixed Lie algebra and lifts them to the Lie group. This yields Trivialized Flow Matching (TFM), Trivialized Consistency Models (TCM), and momentum-based extensions with endpoint correction, enabling flexible path design, simpler few-step objectives, and generation on non-compact Lie groups. We evaluate TGM on compact SO(3) benchmarks, non-compact $\mathrm{Sp}(4,\mathbb{R})$ datasets motivated by continuous quantum systems and paraxial optics, and real-world protein backbone generation. Across these settings, TGM improves sample quality and efficiency over existing Riemannian and Lie group baselines.

Generative recommendation (GR) aligns with advances in generative AI by casting next-item prediction as token-level generation rather than score-based ranking. Most GR methods adopt a two-stage pipeline: (i) \textit{item tokenization}, which maps each item to a sequence of discrete, hierarchically organized tokens; and (ii) \textit{autoregressive generation}, which predicts the next item's tokens conditioned on the tokens of user's interaction history. Although hierarchical tokenization induces a prefix tree (trie) over items, standard autoregressive modeling with conventional Transformers often flattens item tokens into a linear stream and overlooks the underlying topology. To address this, we propose TrieRec, a trie-aware generative recommendation method that augments Transformers with structural inductive biases via two positional encodings. First, a \textit{trie-aware absolute positional encoding} aggregates a token's (node's) local structural context (\eg depth, ancestors, and descendants) into the token representation. Second, a \textit{topology-aware relative positional encoding} injects pairwise structural relations into self-attention to capture topology-induced semantic relatedness. TrieRec is also model-agnostic, efficient, and hyperparameter-free. In our experiments, we implement TrieRec within three representative GR backbones, achieving notably improvements of 8.83\% on average across four real-world datasets.

Tree-sliced distances have emerged as scalable alternatives to Sliced Wasserstein distances by projecting probability measures onto tree metric spaces and exploiting closed-form transport on trees. Existing tree-sliced constructions, however, are largely built around first-order Wasserstein geometry. While this choice yields efficient computation, it fixes the discrepancy to an $L^1$-type aggregation of subtree mass imbalances and provides limited control over the geometry used in downstream optimization. We propose Tree-Sliced Orlicz IPM (TS-Orlicz), a tree-sliced framework that replaces the tree-level $W_1$ discrepancy with an Orlicz integral probability metric. Building on the tractable formulation of Orlicz IPMs on trees, TS-Orlicz aggregates Orlicz-induced discrepancies over random tree systems while preserving the scalability of tree-sliced computation. By varying the underlying Orlicz function, the framework recovers $L^p$-type behavior and also supports non-polynomial, tail-sensitive geometries that emphasize large subtree discrepancies. We show that TS-Orlicz preserves key properties of tree-sliced constructions and admits efficient computation via closed-form special cases and one-dimensional scalar optimization. We further extend the framework to probability measures on hyperspheres. Experiments across Euclidean and spherical settings, including gradient flows, self-supervised learning, and diffusion-based generative modeling, show that Orlicz-induced tree-sliced discrepancies achieve competitive or improved performance over sliced and tree-sliced baselines while maintaining low computational cost.

Effective discrete representation learning with VQ-VAE serves as a fundamental component of modern autoregressive generative models. However, it is widely known to suffer from codebook collapse and inefficient code utilization. To address this issue, we propose a simple yet effective alternative to standard vector quantization by formulating neural quantization as a joint modeling and clustering process. Specifically, we learn the latent space using a lightweight flow-matching model alongside training, corresponding to a probability flow ODE that transports an often fixed well-behaved source distribution while preserving probability mass. Based on this, we define the codebook $\mathcal{C}_1$ by transporting even-quantile partitioned prior codes $\mathcal{C}_0$ from the source space through the learned flow, and obtaining the Voronoi centroids under the induced distribution, leading a structured discretization. We evaluated on image tasks, and two tasks require high-precision tokenization, demonstrating scalability and improved expressivity of the codebook with full utilization.

Diffusion models generate samples by denoising along the score of a perturbed target distribution. In practice, one trains a neural diffusion model, which is computationally expensive. Recent work suggests that score matching implicitly smooths the empirical score, and that this smoothing bias promotes generalization by capturing low-dimensional data geometry. We propose moment-matched score-smoothed overdamped Langevin dynamics (MM-SOLD), a training-free interacting particle sampler that enforces the target moments throughout the sampling trajectory. We prove that, in the large-particle limit, the empirical particle density converges to a deterministic limit whose one-particle stationary marginal is a Gibbs--Boltzmann density obtained by exponentially tilting a naive score-smoothed diffusion target. The mean and covariance of this distribution agree with the empirical moments of the training data. Experiments on 2D distributions and latent-space image generation show that MM-SOLD enables fast, robust, training-free sampling on CPUs, with sample fidelity and diversity competitive with neural diffusion baselines.