NeurIPS 2026 论文列表

Knapsack and Top-$k$ operators are useful for selecting discrete subsets of variables. However, their integration into neural networks is challenging as they are piecewise constant, yielding gradients that are zero almost everywhere. In this paper, we propose a unified framework casting these operators as dynamic programs, and derive differentiable relaxations by smoothing the underlying recursions. On the algorithmic side, we develop efficient parallel algorithms supporting both deterministic and stochastic forward passes, and vector-Jacobian products for the backward pass. On the theoretical side, we prove that Shannon entropy is the unique separable binary regularization choice for the local DP smoothing that yields permutation-equivariant operators, and characterize regularizers inducing sparse selections. On the experimental side, we demonstrate our framework on a benchmark on learning to predict Knapsack solutions, an extension of discrete VAEs, and a constrained dynamic assortment RL problem.

Direct diffusion modeling of high-resolution spatiotemporal fields is computationally challenging. Parameter-efficient primitives address this by representing high-dimensional data with a compact set of parameters. In this paper, we construct data-dependent tensor primitives without pretrained compression autoencoders. Our construction starts from Tucker decomposition, which captures low-rank multilinear structure through a core tensor and mode-wise factors. However, Tucker factors are non-unique: the same tensor can be represented by different rotated factors, which complicates generative modeling. We address this issue with orthogonal Procrustes (OP) alignment. Specifically, we select medoid anchor matrices from the data and align the factor matrices to resolve the gauge ambiguity. This yields matrix Grassmannian primitives and tensor Grassmannian primitives that are compact, data-adaptive, and directly decodable by explicit multilinear reconstruction. Theoretically, we prove that the proposed primitive maps are homeomorphisms between low-rank tensors and their corresponding primitive spaces, certifying that the representations are non-degenerate and topologically faithful. Building on these primitives, we propose *Diffusion in Aligned Tensor Space* (DiffATS), a generative framework that trains diffusion models directly on aligned tensor primitives. Across images, videos, and PDE solutions, DiffATS achieves strong unconditional and conditional generation performance while compressing original data by $3.9\times$ to $210\times$, without relying on any pretrained deep compression autoencoders.

Diffusion language models intrinsically fail to capture correlations between decoded tokens, which leads to a harsh trade-off between sampling quality and throughput. To solve this issue, we propose DiLaDiff, a variant of masked diffusion language models with three components: (1) a continuous latent space with semantic capabilities, learned by an auto-encoder fine-tuned from an existing masked diffusion language model; (2) a latent diffusion model learning the prior over the encoder distribution; (3) a consistency model distilling the learned prior into a few-step latent generative model. We show that, even without distillation, our latent-guided diffusion model outperforms the masked diffusion baseline while significantly accelerating inference. Consistency distillation further lowers the computational overhead of continuous diffusion, such that the latent is generated in negligible time compared to discrete decoding.

Diffusion language models (Diffusion-LMs) generate text through iterative denoising, exposing a temporal structure that is largely absent from autoregressive decoding. In this paper, we show that this temporal structure provides a useful control axis for generation diversity: early denoising steps mainly determine high-level semantic trajectories, while later steps refine lexical realization. Motivated by this observation, we propose Time-Annealed Perturbation Sampling (TAPS), a training-free inference strategy that samples nearby conditioning trajectories through time-aware, manifold-constrained perturbations. TAPS encourages semantic branching during early denoising and anneals the perturbation away before refinement, improving exploration while preserving prompt alignment, generation quality, and reasoning ability. Experiments on multiple Diffusion-LM backbones, including non-autoregressive and semi-autoregressive models, show that TAPS consistently improves semantic and lexical diversity across open-ended and instruction-following generation tasks, while preserving reasoning ability on verifiable reasoning benchmarks with negligible overhead.

Neural representations are not unique objects. Even when two systems realize the same downstream computation, their hidden coordinates may differ by reparameterization. A probe family intended to reveal structure already present in a representation should therefore be stable under the relevant representation symmetries rather than be tied to a particular basis. We study this group action in the tractable exact setting of the final readout layer, where equivalent realizations induce affine changes of hidden coordinates. The resulting symmetry principle singles out a unique hierarchy of shallow coordinate-stable probes, with linear probes as its degree-1 member. We also show that a natural object for cross-model probe transfer is a shared probe-visible quotient--the representation modulo directions invisible to the probe family--rather than the full hidden state. Experiments on synthetic and real-world tasks support both predictions, showing where degree-2 probes help beyond linear ones and how quotient-based transfer enables coverage-aware monitor portability across model families. These results point toward a broader geometric representation theory of neural probing, with coverage-aware monitor transfer as a concrete operational consequence.

Phylogenetic inference plays a central role in understanding evolutionary relationships, with applications ranging from tracking pathogen spread to reconstructing the history of life. Conventionally, practitioners obtain posteriors over the phylogenetic tree of species using MCMC methods. However, such likelihood-based methods are only tractable for simple evolutionary models with restrictive assumptions. For more complex and realistic evolutionary models, conventional methods are prohibitively expensive, inaccurate, or even impossible. We instead advocate for a simulation-based inference approach, by using simulated data from an evolutionary model to train a neural network that predicts tree topologies conditioned on sequences. To accurately represent the complex posterior distributions over tree topologies that can arise, we present flexible models that iteratively generate trees using three natural paradigms: top-down, middle-out, and bottom-up. We use a discrete diffusion framework to train these models efficiently on large-scale simulated datasets of phylogenetic trees. For all three generative paradigms, our models fit the data substantially better than the previous state-of-the-art simulation-based method, Phyloformer 2, and obtain more accurate posteriors on real datasets. Finally, our models outperform misspecified conventional methods on data following complex evolutionary processes.

In high-stakes settings, decision-makers using conformal prediction (CP) read the predictive interval's width as their operational uncertainty signal. Local feature attribution methods, applied to that width, silently conflate two semantically distinct contributions: a calibration-driven baseline that depends on the held-out calibration set, and an instance-driven term that depends on the test point. We propose a two-game Shapley construction---one game over feature coalitions at the test point, one over feature coalitions across the calibration set---that decomposes the total attribution into calibration-driven and instance-driven components. The construction is method-agnostic on two axes: any local attribution method that can be applied to a scalar uncertainty target can be used, and any split CP family whose uncertainty size admits a known separation into a calibration-only and an instance-only summary satisfies the decomposition. Empirically, the calibration-driven and instance-driven attributions frequently carry opposite signs on synthetic and real data, with representative cases where a feature's sign reverses between the two views; the total attribution then becomes a misleading sum. On a clinical-decision task with semi-synthetic data, this conflation degrades decision quality, whereas jointly considering the calibration-driven and instance-driven attributions recovers high-uncertainty cases missed by total attribution. We further empirically verify that the decomposition holds across multiple CP families that satisfy the separability conditions.

Generative visual verifiers play a crucial role in advancing multimodal intelligence systems. In this paper, to enhance the robustness of visual verifiers in complex and realistic open-world scenarios, we move beyond conventional binary verifiers that produce only True/False discrete judgments. Instead, we introduce a verifier that automatically decomposes complex prompts or environmental rules into fine-grained components and assigns pointwise scores, thereby providing a continuous and more informative critique signal. Under a general reinforcement learning framework, we first empirically demonstrate that the proposed pointwise decomposed verifier significantly outperforms binary verifiers in traditional text-to-image scenarios. We then extend our investigation to a novel paradigm: generative world modeling, where generative models are leveraged for world simulation and world reasoning. From a theoretical standpoint, we further show that when ground-truth images are easy to obtain, a pairwise verification paradigm yields more accurate critiques than the pointwise formulation. Empirical results on diverse world-modeling tasks, such as Maze and Sudoku, further validate the effectiveness of our approach. Overall, our findings suggest a key insight: the transition from generative models to world-modeling agents critically hinges on the availability of accurate pairwise decomposed visual verifiers.

We propose D-DOIT (Discrete Doob-Oriented Inference-time Transformation), a training-free and efficient adaptation method for discrete diffusion models with generic rewards. D-DOIT formulates adaptation as sampling from a reward-tilted target distribution and realizes this transport through Doob's h-transform of the discrete diffusion reverse kernel, using only reward values rather than reward gradients. Unlike continuous diffusion, masked discrete diffusion samples categorical token-reveal transitions rather than continuous state updates. D-DOIT derives the corresponding discrete Doob's h-transform, which guides sampling by reweighting reverse transition probabilities instead of adding a drift correction. To make this transformation practical, D-DOIT avoids expensive future rollouts. At each guided step, D-DOIT samples candidate next states, uses the model prediction head to complete each candidate into a clean sequence, evaluates each completion with the reward oracle, and resamples the next state with probabilities proportional to the rewards. An optional late-stage best-of-$K$ refinement further improves sample quality by branching trajectories only near the end of denoising, avoiding the $K$-fold cost over the full trajectory. Empirically, on regulatory DNA sequence design benchmarks, D-DOIT consistently outperforms training-free guidance baselines and achieves performance competitive with training-based methods, improving both enhancer activity and cell-type-specificity while preserving sequence naturalness.

We introduce cyclic denoising—repeated forward and reverse diffusion at controlled noise amplitudes—as an extraction attack for image diffusion models. Inspired by random organization in disordered solids, where cyclic mechanical perturbations anneal the system into increasingly stable configurations, cyclic denoising exposes regions of the learned distribution that remain largely inaccessible to standard sampling. We find that this dynamics drives samples toward attractors with a broad stability spectrum, with the deepest attractors exhibiting ultrastability: they can be regenerated from near-total corruption and sustained through thousands of noising-denoising cycles. Many of these deep attractors correspond to memorized training images, including stock photographs, brand watermarks, and web-crawl artifacts. Our extraction attack requires sampler-level control, including mid-process noise injection, but no gradients and no weight inspection. Crucially, it requires no prior knowledge of training data, captions, or prompts. In contrast, prior generate-and-filter attacks commonly rely on prompted generation using known or suspected training captions, followed by large-scale sampling and post-hoc similarity or membership-inference filtering. While cyclic denoising can also be applied with prompts, our main protocol is fully unconditioned. We demonstrate the phenomenon in Stable Diffusion v1.4, a large latent diffusion model, and in a smaller pixel-space DDPM, showing consistent behavior across latent- and pixel-space diffusion models. Across noise amplitudes, we observe a dynamical transition from trivial fixed points to structured memorized images, hierarchical partial absorption in which coarse scene layout freezes while fine details remain diffusive, basin hopping between memorized states with long residence times, prompt-stabilized memorized templates, and cross-initial-condition universality of the recovered attractor set. Together, these results establish cyclic denoising as both a physics-inspired probe of generative landscapes and a practical tool for memorization auditing, with implications for privacy, copyright compliance, and model fingerprinting.

Crystal generative models mainly learn what stable crystals look like, with little explicit supervision for what makes them stable. We reveal a substantial representation gap between state-of-the-art crystal generative models and pretrained universal machine learning interatomic potentials (MLIPs) via energy probing, and show this gap can be closed by a simple training-time alignment. We propose Crystal REPresentation Alignment (CrystalREPA), a plug-and-play framework that aligns the atom-wise hidden states of generative encoders with frozen MLIP representations through an element-aware contrastive objective, transferring stability-aware atomistic priors with marginal training overhead and no additional inference cost. Across three generative frameworks, ten MLIP teachers, and two benchmark datasets, CrystalREPA consistently improves the thermodynamic stability, structural validity, and structural fidelity of generated crystals. Equally important, we find that an MLIP's transfer effectiveness is poorly predicted by its accuracy on standard leaderboards (e.g., Matbench Discovery) but strongly predicted by the distinguishability of its atom-wise representation space, yielding a practical, accuracy-independent criterion for selecting MLIP teachers for generative transfer.

Multi-Level Intermediate Representation (MLIR) underlies modern ML compiler infrastructure, including TensorFlow, JAX via StableHLO, PyTorch's Inductor backend, and IREE. Yet it appears only in trace amounts in code-LM pretraining corpora. MLIR is also extensible by design: new dialects ship per application domain, so maintaining a fine-tuned model per dialect does not scale. We ask whether inference-time priors derived mechanically from each dialect's Operation Definition Specification (ODS) can substitute for gradient-based adaptation. We make two contributions. First, we release four natural-language-to-MLIR benchmarks across three dialects (MLIR-Spec-150, Linalg-Spec-30, StableHLO-Spec-30, and StableHLO-Held-Out-200), totaling 410 in-scope NL→MLIR pairs, plus a 25-program StableHLO-OutOfGrammar stress set (435 benchmark instances). Thirty of the Spec prompts, ten per dialect, also carry hand-authored input and expected-output references for functional testing (MLIR-Functional-Reference-30). All artifacts ship under Apache-2.0 with Gebru datasheets and Croissant 1.1 metadata. Second, on top of these benchmarks we build a three-layer schema-derived constraint stack: a context-free grammar over op signatures (C1), type-domain splits from an ODS-extracted type lattice (C2), and an SSA-scope validator driving five-retry rejection sampling (C3). Porting the stack from arith+func+memref+linalg to StableHLO required no new constraint-layer code. Empirically, on dialects whose verifier semantics are dominated by structural constraints, SmolLM2-1.7B with token-level schema-derived constraints matches or exceeds 15B–34B code LMs that run the strongest constraint enforcement their serving stack admits (post-hoc rejection), at a matched retry budget and 8–25× the per-generation speed: on linalg it reaches 80.0% verify-valid (three runs, each 80.0%, n=125), 21 to 44 pp above CodeLlama-34B, Granite-Code-34B, and StarCoder2-15B with non-overlapping CIs, and the lead survives a same-family fp16 precision control. The comparison is between systems, not models: under the baselines' post-hoc protocol, SmolLM2 itself falls from 52.0% to 24.5% on arith+func, a +27.5 pp masking contribution. On arith+func and on the templated parametric StableHLO-Held-Out-200, where verifier semantics turn on attribute values rather than structure, the same baselines match or beat the SLM; we scope these explicitly as non-win cells. We release benchmarks, decoder, every per-prompt generation, and a pinned reproducibility Dockerfile.

We propose Coreset-Induced Conditional Velocity Flow Matching (CCVFM), a generative model that augments hierarchical rectified flow with a data-informed source distribution. Hierarchical flow matching models the full conditional velocity law in velocity space, but its inner flow is asked to transport isotropic Gaussian noise to a multimodal target velocity distribution from scratch. Our key observation is that this inner source can be replaced by a closed-form surrogate built from a coreset of the target. CCVFM first compresses the target into weighted atoms using an entropic Sinkhorn coreset and lifts them to a Gaussian mixture. The induced conditional velocity law is then a closed-form Gaussian mixture that can be sampled without a learned neural sampler. A lightweight correction flow, trained from this exact surrogate source, then refines the remaining surrogate-to-target residual rather than learning an entire noise-to-data map. We prove that the surrogate transport cost equals the target--surrogate Wasserstein gap under an explicit compression assumption, whereas the noise-source analogue has a dimension-scale lower bound. We further characterize the conditional second moment of the direct surrogate-source training target and show that its source-dependent excess is small when the surrogate conditional law is close to the true conditional velocity law in mean and covariance. Empirically, on MNIST, CIFAR-10, ImageNet-32, and CelebA-HQ, the proposed method reaches competitive few-step generation under matched architectures. Codes are available at \url{https://anonymous.4open.science/r/ccvfm-code-11D3/}.

Despite the success of foundation models in language and vision, molecular graph generation still lacks a unified framework for heterogeneous design tasks with reliable controllability. While reinforcement learning (RL) offers a natural post-training mechanism for task-specific optimization, applying it to graph generative models is hindered by the vast atom-wise action spaces and chemically invalid intermediate states. We propose \textbf{Co}ntrollable \textbf{Mole}cular Generative Foundation Models (CoMole), built with a unified motif-aware graph diffusion pipeline. By learning a motif-aware graph space, CoMole transfers pretrained structural priors into controllable generation, where RL optimizes conditional reverse policies over chemically meaningful decisions. We theoretically characterize the bottleneck of atom-level RL and justify motif-aware policy optimization. Across three heterogeneous benchmarks spanning materials and drug discovery, CoMole ranks first in controllability on all nine targets, reduces MAE by up to 48.2\% relative to the strongest baselines, and maintains validity above 0.94 without rule-based correction or post-hoc filtering. We further show that CoMole transfers controllability to unseen properties by optimizing only task embeddings with the generator frozen, achieving performance competitive with strong task-specific baselines.

Missing data is pervasive in real-world datasets, arising from sensor failures, image occlusions, and incomplete reporting. Imputation is a conditional generation problem that must preserve observed entries exactly while producing plausible values for missing ones. Yet most diffusion-based imputers adopt Gaussian noising whose global perturbations are structurally misaligned with this local hard constraint, so consistency is typically enforced through conditional training, clamping, projection, or repainting-style corrections. We address this mismatch with Continuously-Augmented Hybrid Masked Diffusion (CAHMD), a masked diffusion framework whose conditional sampler leaves observed coordinates unchanged by construction. To extend masked diffusion beyond purely discrete data, CAHMD attaches coordinate-wise auxiliary continuous latents to masked entries, providing a denoising channel before values are revealed in continuous and hybrid data. For incomplete training data, we introduce observed-mask gating, an observed-data masked reconstruction principle that uses available entries as pseudo-missing targets and avoids repeated EM-style imputation steps. Across tabular, image, and image--caption benchmarks, CAHMD gives a strong reconstruction--perception--efficiency trade-off while reducing the training overhead of EM-style self-imputation and the inference overhead of repainting-style inner loops.

Existing conditional diffusion models typically inject condition information into the reverse-time denoising process, either as model inputs or through guidance. Although effective for conditional fidelity, this design burdens the denoiser when compact continuous signals, such as user preference ratios or mixture degrees, must support both image reconstruction and condition-wise separation, often degrading sample quality. In this work, we reinterpret this limitation not as a problem of condition representation, but as a problem of condition placement. We propose the Continuous Personalized Diffusion Model (CPDM), which shifts the locus of conditioning from reverse-time signal injection to forward geometry formation by coupling bounded spinor-component coordinates with normalized image-space drift directions. The resulting condition-dependent forward drift forms condition-specific terminal geometry, from which continuous changes along the spinor-component coordinate are reflected as continuous visual transitions rather than endpoint interpolation. Experiments show that, even with a single scalar condition, CPDM achieves competitive performance compared with standard and higher-capacity reverse-conditioning baselines and supports continuous generation under compact scalar control. These results suggest forward geometry design as a practical alternative to conventional reverse-time conditioning for compact continuous personalization.

Real-world generative problems in biology, medical imaging, or robotics, rarely come with perfectly paired source and target distributions. While unbalanced Optimal Transport (uOT) provides a robust framework to bridge unpaired datasets via minimum-length paths in probability space, existing formulations based on the Wasserstein–Fisher–Rao (WFR) geometry introduce a structural bias toward high density regions, often triggering mode collapse. We introduce Contact unbalanced Optimal Transport (CuOT), a novel uOT formulation grounded in contact geometry that decouples density transport from mass growth to eliminate structural bias. This allows CuOT to adapt sampling steps to the local data structure, naturally reducing step sizes in high-density regions to prevent overshooting and ensuring stable convergence. The result is a stable, scalable path-length minimization solver that consistently outperforms WFR-based methods on biological dynamics reconstruction, unpaired image-to-image translation, and video generation.

Diffusion and flow models enable powerful generative modeling, but controlled editing remains challenging due to the need to balance source fidelity and edit compliance along the generative trajectory. We propose a principled, inversion-free framework for flow-based image editing from a trajectory centric perspective. Rather than relying on inversion or heuristic guidance, we introduce a one-step look-ahead mechanism that evaluates the effect of candidate updates on both edit and fidelity rewards estimated via denoising, and adjusts the current update based on this evaluation. At each step, our method applies reward-driven corrections guided by the look-ahead evaluation under an explicit fidelity constraint, resulting in stable and coherent trajectory evolution. This look-ahead design mitigates gradient interference between edit and fidelity objectives by anticipating their interaction in future states, leading to improved trade-offs. Experiments demonstrate that the proposed approach achieves stronger semantic edits while better preserving source content compared to existing strong baselines.

Modern deep learning architectures increasingly contend with sophisticated signals that are natively infinite-dimensional, such as time series, probability distributions, or operators, and are defined over irregular domains. Yet, a unified learning theory for these settings has been lacking. To start addressing this gap, we introduce a novel convolutional learning framework for possibly infinite-dimensional signals supported on a manifold. Namely, we use the connection Laplacian associated with a Hilbert bundle as a convolutional operator, and we derive filters and neural networks, dubbed as \textit{HilbNets}. We make HilbNets and, more generally, the convolution operation, implementable via a two-stage sampling procedure. First, we show that sampling the manifold induces a Hilbert Cellular Sheaf, a generalized graph structure with Hilbert feature spaces and edge-wise coupling rules, and we prove that its sheaf Laplacian converges in probability to the underlying connection Laplacian as the sampling density increases. Notably, this result is a generalization to the infinite-dimensional bundle setting of the Belkin \& Niyogi \cite{BELKIN20081289} convergence result for the graph Laplacian to the manifold Laplacian, a theoretical cornerstone of geometric learning methods. Second, we discretize the signals and prove that the discretized (implementable) HilbNets converge to the underlying continuous architectures and are transferable across different samplings of the same bundle, providing consistency for learning. Finally, we validate our framework on synthetic and real-world tasks. Overall, our results broaden the scope of geometric learning as a whole by lifting classical Laplacian-based frameworks to settings where the signal at each point lives in its own Hilbert space.