NeurIPS 2026 论文列表

Diffusion Maps (DM) is a well studied and popular non-linear dimension reduction algorithm. Surprisingly, while the convergence properties of DM are well understood, the {\em geometric} properties of the embedding, such as reach and smoothness have not yet been studied. Under a set of standard assumptions on a family of submanifolds $\subset \mathbb{R}^D$, we derive a series of geometric properties that are preserved by DM, including almost uniform density, finite polynomial approximation and reach. Leveraging these properties, we establish rigorous bounds on the embedding errors introduced by the DM algorithm, of the order $(\frac{\log n}{n})^{\frac{1}{8d+16}}$. These results offer a solid theoretical foundation for understanding the performance and reliability of DM in practical applications.

Despite their success in image generation, diffusion models can memorize training data, raising serious privacy and copyright concerns. Although prior work has identified empirical factors associated with memorization, such as text guidance, prompt specificity, and duplicated training examples, the mechanism by which memorization is triggered and propagated during denoising remains unclear. In this paper, we provide a theoretical explanation of how memorization occurs in text-to-image diffusion models. We show that conditional overfitting causes the conditional posterior mean to collapse to the memorized training latent, while the unconditional posterior remains close to the zero-centered data mean at the first denoising step. As a result, classifier-free guidance overestimates the clean prediction and injects an amplified memorized signal into the reverse trajectory. We further show that this signal propagates across timesteps because each guided latent is fed back into the denoising network, allowing the conditional branch to indirectly shift the unconditional branch. To characterize this process, we introduce the posterior lag, the discrepancy between conditional and unconditional posterior means. For normal prompts, this lag decreases as the two posteriors synchronize during denoising. For memorized prompts, the conditional posterior commits early to a specific training latent, while the unconditional posterior catches up only later, producing a distinctive rise-and-fall lag pattern. Our analysis provides a mechanism-level explanation of memorization and clarifies why text guidance and early denoising steps play a central role in memorized generation.

Geometric modeling has become an essential paradigm in AI for Science, where data often inhabit intrinsically curved or structured spaces. However, existing manifold generative models often rely on closed-form or tractable access to global geometric primitives, such as geodesic distances, parallel transport, or spectral decompositions, which are rarely available beyond canonical geometries. To overcome this limitation, we propose Horizontal Diffusion Models (HDMs), a score-based generative framework defined on the orthonormal frame bundle of a Riemannian manifold. Instead of requiring global geometric operations, HDM lifts Euclidean diffusion processes through the Levi-Civita horizontal distribution, using only local metric and connection information while preserving intrinsic manifold geometry. This construction allows standard Euclidean score networks to be lifted into geometry-consistent and gauge-equivariant horizontal vector fields, bypassing the need for manifold-specific neural architectures. We further derive a horizontal KL objective that reduces to a Euclidean score-matching loss and analyze the curvature-dependent cost of the lift through a generalization bound. Experiments on parametric surfaces and scientific datasets demonstrate high-fidelity generation across diverse manifolds with nontrivial geometry and topology.

Reconstructing a dynamic 4D scene along a novel camera trajectory requires both metric geometry from the source video and generative completion of disoccluded target-view regions. Feed-forward 4D reconstruction models recover increasingly comprehensive input-view geometry, including depth, point maps, and dense 3D tracks, but remain tied to the observed camera stream. Camera-controlled video diffusion models (VDMs) provide strong generative priors for novel-view synthesis, yet their camera control is typically not precise enough for metric novel-view reconstruction. We argue that comprehensive input-view 4D reconstruction is an effective geometric interface between these two capabilities: properly exposed to a VDM, it turns reconstruction outputs into camera-accurate novel-view RGB videos that remain geometrically consistent under downstream 4D reconstruction. We introduce HOLO4D, a geometry-aware video-to-video framework that controls a pretrained VDM with a hybrid 4D geometric cache built from the source video. A small set of source views covering the camera motion forms the static cache, while dynamic regions are rendered from the matching source frame. The resulting hybrid RGB-D representation is combined with explicit valid masks, target-camera ray embeddings, and dense 3D tracking tokens. Conditioned on this 4D scaffold, the diffusion backbone synthesizes the target-view RGB video. Under a common downstream 4D reconstructor, our generated videos yield target-view depth more consistent with the held-out reconstruction than that of the baselines, and an additional feature-level readout shows that intermediate VAE features already encode target-view depth. Experiments and ablations further show that progressively richer 3D/4D reconstruction signals improve camera adherence.

High-fidelity 3D generative modeling underpins game asset creation, medical imaging, and VR/AR environmental design, where geometric structure directly influences perception and decision-making. Diffusion models represent a powerful paradigm for point cloud generation, yet existing approaches rely heavily on local voxel or patch features and often miss global structural organization. Recent topology-aware methods show that global conditioning can improve generation quality, yet persistent-homology pipelines add substantial preprocessing complexity. We introduce HilbertGen-3D, a topology-aware conditional diffusion framework based on Hilbert–Multifractal Conditioning (HMC). HMC computes multi-scale voxel measures, serializes them via a 3D Hilbert curve to expose structured spatial dependencies, and estimates the generalized fractal dimensions from scale-dependent partition functions. We encode these signals as global embeddings and multi-scale tokens, and inject them into a diffusion denoiser through an efficient bottleneck fusion module. On ShapeNet dataset, HilbertGen-3D reduces the 1-Nearest Neighbor Accuracy by up to 8.74 points and improves coverage by up to +21.45 over prior topology-aware methods. This shows that combining local density cues with global Hilbert–multifractal structure provides a simple, efficient, and effective recipe for high-fidelity and diverse 3D generation.

Adapting pretrained diffusion models to downstream objectives such as inverse problems often requires expensive test-time guidance or optimization. We propose a principled framework for generating high-quality reward-aligned samples at substantially reduced inference cost. Our approach formulates test-time adaptation as a hierarchical variational model, where control is amortized into a lightweight yet expressive stochastic policy. This formulation naturally supports few-step diffusion sampling: large step sizes enable fast inference, while the learned policy maintains sample quality by providing structured per-step control. The resulting fully amortized sampler achieves a strong quality--speed tradeoff, matching or exceeding recent test-time scaling baselines while requiring significantly less compute. For example, on $4\times$ super-resolution, our method achieves better perceptual quality with more than 5$\times$ faster inference compared to the best-performing baseline. We further extend our approach to a semi-amortized regime that combines cheap amortized proposals with limited test-time optimization, achieving state-of-the-art perceptual quality across several challenging inverse problems.

Heavy-tailed data arise in many domains where rare events carry disproportionate importance, such as imbalanced image datasets, financial returns, and weather extremes. Standard diffusion and flow-matching models typically begin from Gaussian noise or Gaussian source distributions, which yield tractable training targets but provide a poor inductive match for heavy-tailed data. We propose Heavy-Tailed Flow Matching via Random Clocks (HTFM), a framework that portrays heavy-tailed sources as mixtures of clock-conditioned Gaussian sources. Conditioning on a given clock path, the source distribution and flow are Gaussian; marginalizing over the clock gives a Gaussian scale mixture covering Gaussian, $\alpha$-stable, and Student-t families. To make the clock-conditioned vector field practical, we encode the path-valued clock using truncated logsignature features, allowing the velocity field to adapt to the realized conditional space with negligible overhead. Empirically, on 2D imbalanced $\alpha$-stable mixtures, CIFAR10-LT, and HRRR weather fields, HTFM improves mode coverage, sample quality, and tail-statistic recovery over Gaussian flow matching and competitive heavy-tailed baselines, while retaining the low-NFE sampling advantage of flow matching. Moreover, the random-clock formulation further provides a practical tail-control interface: by varying only the clock law or tail parameter, the same architecture can calibrate the ``heaviness'' of generated tails across different distribution families.

Recent image generation models produce photo-realistic results with rich details, but transferring their powerful priors to video restoration remains difficult due to temporal inconsistency from stochastic detail synthesis. Existing video restoration methods improve temporal coherence but often sacrifice visual fidelity, leaving a gap between image-level quality and video-level stability. We propose a generative video restoration method that bridges this gap by enabling temporally consistent detail synthesis from image generation priors. Our method combines noise energy rebalancing to suppress structure-disturbing low-frequency stochasticity, motion-aligned noise warping to propagate details along object motion, a self-supervised denoising encoder to mitigate encoder-induced temporal uncertainty, and decoupled temporal attention to model cross-frame dependencies. Together, these components preserve fidelity, enhance fine-grained realism, and maintain temporal consistency. Extensive experiments show that our method substantially outperforms existing video restoration approaches in visual quality, detail richness, and temporal stability.

Molecular docking requires reasoning jointly about ligand pose and protein flexibility. Most diffusion-based docking models predict torsional updates with generic Euclidean heads that ignore the periodic geometry of angular variables. This mismatch is especially limiting in flexible docking, where ligand conformations and pocket side chains co-adapt to form the bound complex. Here, we introduce Harmony, a harmonic torsional diffusion framework for flexible protein-ligand docking. Harmony parameterizes ligand and side-chain torsional score fields as derivatives of learned harmonic potentials on the circle, whose noise-level dependence is supplied analytically by the heat semigroup of variance-exploding diffusion on the torus. This construction makes periodicity explicit, removes the need to learn noise conditioning for torsional updates, and gives the model a frequency-aware inductive bias over rotameric motion. On the PDBBind benchmark, Harmony improves ligand pose accuracy and pocket all-atom reconstruction over recent flexible docking methods. On PoseBusters, it improves the physical validity of generated complexes. Case studies on EBNA1 and KRAS G12D illustrate the method's behavior on a polar and a shallow binding site, respectively. Together, these results indicate that aligning the score parameterization with the geometry of the diffusion process is a simple and effective lever for improving flexible docking.

Individual-level genotype data underpin genetic discovery, disease-risk modeling, and therapeutic development, yet many critical settings remain data-limited, including underrepresented ancestries, rare or imbalanced disease cohorts, and restricted-access biobanks. Conditional synthetic genome generation would support privacy-aware benchmarking, simulation, and data augmentation, but requires learning an ultra-high-dimensional discrete distribution over hundreds of thousands to tens of millions of correlated single-nucleotide polymorphisms (SNPs), or sites of DNA variation. We introduce $\mathbf{HELICS}$: $\mathbf{H}$igh-fidelity g$\mathbf{E}$neration via $\mathbf{L}$atent $\mathbf{I}$nterpolant $\mathbf{C}$onditional $\mathbf{S}$ynthesis, a phasing-free latent flow matching framework for genome-wide SNP-level generation from biobank-scale genotype data. HELICS tokenizes chromosomes with convolutional autoencoders, reducing $>$$600{\rm K}$ SNPs to $4{,}096$ continuous latent tokens, and trains a transformer parameterized conditional flow matching model over the concatenated multi-chromosome latent representation. Trained on roughly $428\rm K$ genomes in the UK Biobank, HELICS generates genome-wide synthetic cohorts without haplotype phasing and achieves stronger fidelity to held-out real genotypes than existing haplotype- and genotype-based simulators, including the highest validation allele-frequency agreement ($R^2=0.992$) and superior preservation of local and long-range SNP correlation structure. Conditioning on ancestry and genetic liability summaries enables targeted generation across genetic risk profiles; in perturbation analyses, by increasing the conditioned disease trait liability, HELICS induces SNP-level dosage changes in generated genomes that are highly correlated with published association weights. HELICS provides a scalable generative modeling framework for SNP-level genome data and a path toward conditional synthetic cohorts for data-limited genetic studies.

Classifier-free guidance (CFG) has become a widely adopted and practical approach for enhancing generation quality and improving condition alignment. Recent studies have explored guidance mechanisms for unconditional generation, yet these approaches remain fundamentally tied to assumptions specific to diffusion models. In this work, we propose a spectrum weakening framework for visual autoregressive (AR) models. The method is training-free and condition-free by constructing a controllable weak model in the spectral domain without architectural modifications. We theoretically show that invertible spectral transformations preserve information, while selectively retaining only a subset of the spectrum introduces controlled information reduction. Based on this insight, we perform spectrum selection along the channel dimension of internal representations, which avoids the structural constraints imposed by diffusion models. We further introduce a spectrum-renormalization technique that maintains numerical stability during the weakening process. Comprehensive empirical and ablation studies confirm the effectiveness of our approach, including raster-scan, random-order, and scale-wise AR, spanning discrete and continuous modeling and covering class and text-condition scenarios, demonstrating high-quality unconditional generation and strong prompt alignment maintenance for conditional generation. Code will be made available.

Generating egocentric video from a single exocentric video is an emerging and important topic for AR/VR and physical AI. Compared with conventional novel view synthesis, exo-to-ego generation is a significantly harder task due to the extreme viewpoint changes, extensive occlusions and unobserved regions, where standard geometric conditioning becomes highly unreliable. We present Grounded-Exo2Ego, a principled framework that addresses these challenges at both the architectural and data levels. Architecturally, Grounded-Exo2Ego is a dual-branch video diffusion model that couples a geometric anchoring branch, which renders a 3D reconstruction into the ego view for overall scene layout, with a semantic grounding branch, which anchors per-object context onto the scene geometry so that heavily distorted regions and unobserved regions can be hallucinated in context. Additionally, to support robust training at scale, we substantially improve the labeling pipeline for real-world data and further develop a fully automated synthetic data engine that renders high-quality dynamic humans in procedurally generated environments. Evaluations on the challenging EgoExo4D dataset show that our method substantially outperforms recent state-of-the-art approaches. Extensive ablations further demonstrate that both structured semantic grounding and rigorous data processing are essential for robust exo-to-ego video generation in extreme scenarios.

Generative modeling of discrete data, such as graphs, underpins many scientific and industrial applications, including molecular discovery and materials design. In these domains, probabilistic inference is particularly valuable, as it enables composable generation and principled incorporation of desired constraints, such as structural or functional properties. Energy-based models naturally support this goal by capturing relative likelihoods and enabling composable inference by directly enforcing constraints during inference. However, discrete energy-based models typically struggle with efficient and high-quality sampling, as off-support regions often contain spurious local minima, trapping samplers and causing training instabilities, resulting in a fidelity gap compared to discrete diffusion models. To address this gap, we introduce Graph Energy Matching (GEM), a discrete generative framework inspired by the Jordan--Kinderlehrer--Otto (JKO) transport-map optimization perspective. GEM learns a permutation-invariant potential energy that simultaneously guides discrete transport from noise toward high-likelihood graph regions and refines samples within these regions. We further introduce a sampling protocol leveraging an energy-based switching strategy, seamlessly bridging rapid, gradient-guided transport and a local mixing regime for effective exploration. On molecular graph benchmarks, GEM matches or surpasses strong discrete diffusion baselines on most reported metrics. Beyond improving generation quality, GEM's relative likelihood modeling enables targeted exploration, facilitating compositional generation, property-constrained sampling, and interpolation between graphs.

Finding frequently occurring subgraph patterns or network motifs in neural architectures is crucial for optimizing efficiency, accelerating design, and uncovering structural insights. However, as the subgraph size increases, enumeration-based methods are perfectly accurate but computationally prohibitive, while sampling-based methods are computationally tractable but suffer from a severe decline in discovery capability. To address these challenges, this paper proposes GraDE, a diffusion-guided search framework that ensures both computational feasibility and discovery capability. The key innovation is the $\underline{\textnormal{Gra}}\textnormal{ph}$ $\underline{\textnormal{D}}\textnormal{iffusion}$ $\underline{\textnormal{E}}\textnormal{stimator}$ (GraDE), which is the first to introduce graph diffusion models to identify frequent subgraphs by scoring their typicality within the learned distribution. Comprehensive experiments demonstrate that the estimator achieves superior ranking accuracy, with up to 114\% improvement compared to sampling-based baselines. Benefiting from this, the proposed framework successfully discovers large-scale frequent patterns, achieving up to 30$\times$ higher median frequency than sampling-based methods.

Glycosylation is among the most diverse and important post-translational modifications in biology, governing immunogenicity, self-recognition, and the clinical viability of biologic drugs. Glycans cannot be sequenced from a template, and de novo structure prediction from tandem mass spectrometry (MS/MS) remains a longstanding bottleneck. The current state of the art, GlycoBART, is a $207$M autoregressive transformer whose $O(\mathrm{beam} \cdot \mathrm{output\_length})$ decoder passes preclude real-time annotation. We introduce $\textbf{GlycoGen}$, a $50$M Discrete Flow Matching (DFM) model that predicts glycan structure from MS/MS spectra by direct, non-autoregressive generation in a few parallel forward passes. We pair it at inference time with $\textbf{Crystallizing Flows}$, a deterministic sampler that propagates the per-token distribution on the probability simplex and freezes each token to a one-hot (*crystallizes* it) the moment its argmax leaves the mask, exiting early once all tokens are unmasked. The sampler feeds the denoiser mixture embeddings, and runs out-of-the-box with no retraining. GlycoGen + Crystallizing Flows reach $\mathbf{0.9266}$ top-1 structural accuracy on the CandyCrunch test set, three orders of magnitude faster than GlycoBART, Pareto-dominating the prior state of the art on *both* accuracy *and* speed. We extend our experiments to a matched-architecture MDLM denoiser (Sahoo et al. 2024) and observe a comparable lift: the sampler generalizes from continuous-time flow matching to discrete-time masked diffusion. To our knowledge, this is a new state of the art for de novo open-vocabulary glycan structure prediction, and the first system fast enough for accurate real-time inline annotation on modern LC-MS/MS instruments.

Diffusion large language models (LLMs) have recently emerged as a promising alternative to autoregressive LLMs, enabling parallel generation through iterative denoising. Recent guidance methods improve diffusion LLMs by introducing a weak model to guide the prediction of the base model during denoising. However, the influence of the weak model during denoising remains less clear, and computing its prediction requires an additional forward pass at each denoising step. We present in this paper an in-depth analysis of how diffusion LLMs use contextual information during denoising. Our analysis reveals that diffusion LLMs rely more heavily on local context while often underutilizing global context. Based on this observation, we introduce Global Context Guidance (GCG), a feature-space guidance method that enhances global-context utilization without constructing an explicit weak model. Extensive experiments on LLaDA-8B, Dream-7B, and LLaDA-1.5 across diverse benchmarks demonstrate that GCG consistently outperforms existing guidance methods, while incurring much lower inference overhead. We will release our code upon acceptance.

Similarity measures such as canonical correlation analysis (CCA), representational similarity analysis (RSA) and center kernel alignment (CKA), are widely used to compare the representational geometries used by different neural networks to solve the same task. Yet, because existing methods compare the *extrinsic geometry* of neural representations in state space, rather than their *intrinsic geometry*, they may fail to capture subtle yet crucial distinctions between fundamentally different computations performed by biological and artificial neural networks. Here, we introduce metric similarity analysis (MSA), a novel method which leverages tools from Riemannian geometry to compare the intrinsic geometry of neural manifolds. Within our mathematical framework, we derive several properties of MSA, including coordinate, scale and rotation invariances. We show that MSA can be used to i) disentangle neural computations of deep networks in rich vs. lazy learning regimes, ii) compare the computation-through-dynamics of recurrent neural networks and state-space models during neuroscience working memory tasks, and iii) investigate the statistical manifolds of diffusion models. Overall, we introduce a mathematically grounded and broadly applicable framework to understand the mechanisms behind neural computations by contrasting their Riemannian geometries, with broad applicability to both neuroscience and machine learning.

Out-of-distribution (OOD) detection identifies test samples that fall outside a model's training distribution, a capability critical for safe deployment in high-stakes applications. Standard OOD detectors are trained on a specific in-distribution (ID) dataset and detect deviations from that single domain. In contrast, we study few-shot cross-domain OOD detection: given a \emph{single} pre-trained model, can we perform OOD detection on \emph{arbitrary} new ID-OOD task pairs using only a handful of ID samples at inference time, with no additional training? We propose \textbf{UFCOD}, a unified framework that achieves this goal through information-geometric analysis of diffusion trajectories. Our key insight is that diffusion noise predictions are score functions (gradients of log-density), and we extract two energy features: \emph{Path Energy} (integrated score magnitude) and \emph{Dynamics Energy} (score smoothness), that form a discrete Sobolev norm capturing how samples interact with the learned diffusion process. The central contribution is a \textbf{train-once, deploy-anywhere} paradigm: a diffusion model trained on a single dataset serves as a universal feature extractor for OOD detection across semantically unrelated domains. At deployment, each new task requires only $\sim$100 unlabeled ID samples for inference: no retraining, no fine-tuning, no task-specific adaptation. Using 100 ID samples per task, UFCOD achieves 93.7\% average AUROC across 12 cross-domain benchmarks, competitive with methods trained on 50k--163k samples, demonstrating $\sim$500$\times$ improvement in sample efficiency. See our code in \url{https://anonymous.4open.science/r/UFCOD-22E8/README.md}.

Flow matching learns a velocity field whose ordinary differential equation transports a simple reference distribution to a data distribution. Existing theory typically controls this velocity through ambient, isotropic Lipschitz regularity, which becomes extremely pessimistic when data concentrate near a low-dimensional manifold. In this regime, standard error bounds can blow up drastically near the terminal time and fail to explain why flow matching should remain stable. We study flow matching for distributions obtained by smoothing a density on a compact manifold with small Gaussian noise. Our first result is a tube-local Lipschitz regularity theorem showing that, on the relevant neighborhood of the manifold, the population flow-matching velocity has a Jacobian bound that grows only at the inverse effective noise scale. This improves substantially over the stronger singular behavior suggested by existing ambient analyses. Our second result gives a directional description of the velocity Jacobian: tangential directions exhibit mild growth, normal directions are strongly contractive, and tangential-normal coupling is lower order. This reveals that the apparent singularity is highly structured rather than uniformly harmful. These results provide geometric foundations for sharper stability guarantees and suggest a path toward intrinsic-dimension generalization bounds for flow matching on manifold-concentrated data.