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NeurIPS 2026

Watermarking as a Learned Intrinsic Property of Diffusion Models

Xiang Li, Dong-Dong Wu, Masashi Sugiyama, Lannan Luo, Qiang Zeng

Recent advances in latent diffusion models have enabled high-quality image generation, but also raise critical concerns for intellectual property protection in model distribution scenarios, where downstream users have unrestricted access to models, allowing arbitrary modifications. Existing watermarking methods either rely on inference-time control of inputs (e.g., specific prompts or noise initialization) or embed watermark signals in auxiliary components, making them easily removable in such settings. In this paper, we propose INMARK, which treats watermarking as an intrinsic property learned by the model. Instead of relying on input control or auxiliary watermarking components, INMARK enables the core denoising network to internalize and reproduce watermark patterns. Extensive experiments demonstrate that INMARK achieves strong generation fidelity, high watermark detectability, and robustness against attacks, while remaining fully compatible with standard diffusion training pipelines. Our results highlight a new perspective on diffusion model watermarking: the denoising network can learn a reliable and persistent watermarking capability, which is crucial in practical model distribution scenarios.

NeurIPS 2026

Watermarking Without Standards Is Not AI Governance

Alexander Nemecek, Yuzhou Jiang, Erman Ayday

Watermarking has emerged as a leading technical proposal for attributing generative AI content and is increasingly cited in global governance frameworks. This position paper argues that current implementations risk serving as symbolic compliance rather than delivering effective oversight. We identify a growing gap between regulatory expectations and the technical limitations of existing watermarking schemes. Through analysis of policy proposals and industry practices, we show how incentive structures disincentivize robust, auditable deployments. To realign watermarking with governance goals, we propose a three-layer framework encompassing technical standards, audit infrastructure, and enforcement mechanisms. Without enforceable requirements and independent verification, watermarking will remain inadequate for accountability and ultimately undermine broader efforts in AI safety and regulation.

NeurIPS 2026

Watermarking Game-Playing Agents in Perfect-Information Extensive-Form Games

Juho Kim, Fei Fang, Tuomas Sandholm

Watermarking techniques for large language models (LLMs), which encode hidden information in the output so its source can be verified, have gained significant attention in recent days, thanks to their potential capability to detect accidental or deliberate misuse. Similar challenges involving model misuse also exist in the context of game-playing, such as when detecting the unauthorized use of AI tools in gaming platforms (e.g., cheating in online chess). In this paper, we initiate the study of how game-playing strategies can be watermarked. We show how the KGW watermark for LLMs can be adapted to watermark game-playing agents in perfect-information extensive-form games. The watermark can then be detected using a statistical test. We show that the degradation in the quality of the watermarked strategy profile, quantified by the expected utility, can be bounded, but there is a tradeoff between detectability and quality. In our experiments, we bootstrap the watermarking framework to various chess engines and demonstrate that a) the impact of the watermark on the quality of the strategy is negligible and b) the watermark can be detected with just a handful of games.

NeurIPS 2026

Watching Itself Watch: Self-Auditing Visual Reliance for Video Reasoning

Rohan Dugad, Romy Luo, Kristen Grauman

Video reasoning has a distinctive structure: in a chain of thought over video, most tokens follow from prior text, but a small minority hinge on specific moments of the visual input---and which tokens those are varies from one example to the next. Current post-training procedures like GRPO supply supervision that is coarse in exactly this dimension, applying a single scalar reward uniformly across the trajectory while requiring many rollouts and/or costly external judge models. Our key observation is that a model can audit its own visual reliance: at any position, the shift in its next-token distribution when the video is removed from context measures how much that prediction actually used what was seen. Computing this quantity for both a student and a privileged teacher yields a per-token \emph{reliance gap} that localizes positions at which the teacher's predictions depend on the video and the student's do not. We introduce Visually-Aware On-Policy Self-Distillation (VIOS), which turns this self-auditing signal into dense per-token supervision recovered from a single rollout of a single model---no external reward, judge, or larger teacher required. VIOS combines three components: an exponential moving average (EMA) teacher that co-evolves with the student to avoid the ceiling of a frozen rationalizer; a contrastive term that increases the student's sensitivity to the video input; and a reliance gap gate that concentrates supervision on the positions identified. Across 12 benchmarks spanning general, temporal, spatial, knowledge, and long-video understanding, VIOS consistently outperforms its base model and contemporary video-reasoning systems while training in over $9\times$ fewer steps.

NeurIPS 2026

Wasserstein residuals: Learning Gradient Flows from Population Dynamics

Markus Heinonen, Yair Shenfeld, Ricardo Baptista, Daniel Waxman, Dmitry Batenkov, Tim Cooijmans, Elias Bingham

Reconstructing population dynamics is a central problem in the physical and data sciences. Often, the dynamics are modeled as a Wasserstein gradient flow (WGF): a curve of distributions driven by an energy functional. Though there are multiple mathematical characterizations of a WGF, the dominant algorithmic approach relies on the Jordan--Kinderlehrer--Otto (JKO) scheme. JKO-based methods are inflexible to time discretisation and require solving costly optimal transport problems. We take a residual approach, enforcing that the continuity equation conditions are satisfied via a non-negative loss function, whose minimum is the WGF. Combined with a data-fitting divergence, this gives a single global objective. This perspective unifies several existing methods, and leads us to discover a new particle-based method, \emph{stitching}, that is simulation-free and robust to large gaps in observation times of the dynamics. We demonstrate that the stitching method achieves state-of-the-art performance across trajectory inference benchmarks.

NeurIPS 2026

Wasserstein Gradient Flows and Forward-Only Diffusion Are Not Enough for Multimodal Sampling

Daniel McBride, Pratik Khandagale, Cristina Garcia-Cardona, Yen Ting Lin

There has been a plethora of algorithms proposed that leverage Wasserstein gradient flows or forward-only diffusion processes to perform sampling tasks. These approaches are often characterized by theoretical guarantees of exponentially fast convergence to the target distribution. In this work, we study the mixing behavior of this family of sampling methods. By invoking the Jordan--Kinderlehrer--Otto scheme and Otto calculus, we first establish that Wasserstein gradient flow and forward diffusion-based samplers share the same density evolution. Consequently, their convergence can be characterized by studying the convergence behavior of the associated diffusion process, which has been extensively analyzed in nonequilibrium statistical physics. We perform two independent and well-established analyses for this purpose, namely spectral analysis and mean first-passage time analysis. We show that, although the sampling distributions converge to the target distribution exponentially fast, the presence of multimodality can lead to exponentially long mixing times associated with small spectral gaps. Further analysis elucidates that even when combined with annealing, this family of samplers still requires impractically long time to sample multimodal distributions. We discuss the origin of this behavior as a consequence of the local (i.e., gradient-driven) dynamics underlying this class of samplers, and highlight the need for non-local mechanisms to facilitate the transport of probability mass across modes, enabling efficient exploration in multimodal settings.

NeurIPS 2026

Walking the Hypercube: Unbiased Quantum Partition Functions Without the Matrix

Kumar Avinava Dubey, Arijit Sehanobish, Krzysztof M Choromanski

Computing the partition function $\mathcal{Z} = \mathrm{tr}(e^{-\beta H})$ of a quantum spin Hamiltonian $H$ on $n$ sites is a fundamental problem in statistical physics and quantum chemistry. However exact evaluation requires $O(8^n)$ time and $O(4^n)$ memory making it intractable for all but the smallest systems. We propose an unbiased stochastic estimator of $\mathcal{Z}$, and more generally of $\mathrm{tr}(f(H))$ for any function $f$ admitting a convergent power series over exponentially large, implicitly defined operators using only local random walks, avoiding both matrix materialization and matrix-vector products. Our approach combines Graph Random Features with the Hutchinson's stochastic trace estimator, and exploits the algebraic structure of quantum spin Hamiltonians to reduce the per-step computational cost to $O(n + d)$, where $d$ is the mean degree of the spin coupling graph, independent of the Hilbert space dimension $N = 2^n$. We validate the estimator empirically against exact matrix exponentiation for small system sizes, and demonstrate its applicability to system sizes where exact methods are infeasible.

NeurIPS 2026

Walking Through 3D Spaces: Spatial Routing for Referring 3D Gaussian Splatting Segmentation

Peilin Ji, Changshuo Wang, Yong Zhang, Shuting He

This paper introduces Walk3D, a novel 3D Gaussian Splatting (3DGS) framework explicitly designed for 3D referring segmentation, particularly excelling at interpreting complex, long-sentence descriptions. Our primary motivation stems from observing that existing 3DGS-based open-vocabulary methods mainly focus on simple, category-level object segmentation. These methods struggle to precisely segment targets described by highly detailed, multi-sentence queries due to weak compositional language understanding and a lack of structural scene awareness. To tackle these dense and complex linguistic constraints, we propose a spatial routing network that decodes these queries into sequential chain-of-thought instructions upon a scene graph. Specifically, we construct a static supernode graph based on the geometric and semantic properties of the 3DGS space, where a spatial Graph Neural Network (GNN) dynamically pathfinds using the decomposed linguistic chain to accurately segment the referred target. Extensive experiments on complex 3D referring segmentation benchmarks demonstrate the superiority of our proposed method in interpreting lengthy, multi-conditional queries. Our code and trained models will be publicly released.

NeurIPS 2026

WURI: Watching Unfolding Risk in Agent Interactions

Yiyang Duan, Tiantong Wu, Yurong Hao, Wei Yang Bryan Lim

Large language model (LLM) agents increasingly operate through multi-step tool-use trajectories, where harmful intent may be distributed across actions that appear benign in isolation. This challenges single-step moderation, while repeated LLM-as-judge evaluation over growing prefixes can be costly and may intervene too late. We introduce *WURI* (*Watching Unfolding Risk in Agent Interactions*), a lightweight monitor for early prefix-level detection of harmful agent trajectories. WURI encodes each observed textual step with a frozen text encoder, learns an atom-adapted trajectory representation through metric learning, and scores each prefix with a fixed prototype-margin rule. It requires no access to agent model weights or hidden states, does not modify the agent's internal model, and uses no external LLM-as-judge calls at inference. Across five generalization settings, WURI achieves the best average prefix-area under the detection curve (AUDC), ranks first on three settings, and reaches the strict early-detection operating point within four steps in multiple evaluation settings. Runtime analysis shows a wall-clock speedup of over two orders of magnitude compared with repeated full-prefix guardrail evaluation. These results demonstrate that representation-based prefix scoring is an effective and efficient direction for monitoring unfolding risk in LLM agent interactions.

NeurIPS 2026

WTF?! Simulation-Free Reinforcement Learning with Wasserstein-Tilted Flow Maps

Abbas Mammadov, Jerry Huang, Justin Lin, Partha Kaushik, Sheel Shah, Kartik Nair, Yee Whye Teh, Nicholas Boffi

Fine-tuning aims to update a pre-trained flow-based generative model to improve the downstream reward of its generated samples. Existing methods typically frame this problem as sampling from a reward-tilted distribution, which arises as the solution to a KL-regularized reward-maximization problem. Here we take an alternative approach and introduce an *optimal transport* regularizer built directly from the pre-trained drift; we show that the resulting fine-tuning problem is equivalent to a *deterministic optimal-control problem* on the flow. Assuming access to a pre-trained flow map, we exploit this equivalence to devise a simulation-free reinforcement-learning algorithm for fine-tuning generative flows. We call the resulting framework **Wasserstein-Tilted Flow Maps (WTF)**, the first end-to-end fine-tuning recipe native to flow maps. The output of our approach is itself a fine-tuned flow map, retaining few-step reward-aligned inference at deployment. Numerical experiments at text-to-image scale highlight both the efficiency and the efficacy of our approach. More broadly, our work argues that accelerated samplers such as flow maps are essential infrastructure for efficient post-training, and that the dominant KL-regularized formulation of fine-tuning is only one of many choices worth revisiting.

NeurIPS 2026

WORD: Diffusion-Based Posterior Inference for Online Goal Recognition

Almog Anschel, Sarah Keren

Goal recognition is the task of inferring an agent's intended goal from its observed behavior. Existing work has largely focused on high-level symbolic recognition, abstracting away the continuous motion through which agents reach their goal. Methods that do reason over real-world trajectories, rely on an explicit dynamics model that is hard to acquire and rarely transfers across settings. Neither approach explicitly learns how agents move toward each candidate goal, limiting accuracy on ambiguous trajectory prefixes where such knowledge is most needed. We present WoRD (Waypoint Recognition with Diffusion), which uses a learned trajectory prior to infer the agent's goal from partial observations. At each step, WoRD runs one warm-started denoising chain per candidate goal, steers each chain toward the observed trajectory through a closed-form log-likelihood gradient, and reweights the resulting samples by Bayes' rule into a calibrated posterior over goals. We evaluate WoRD on simulated robot settings, pedestrian trajectories, and vehicle trajectories using four metrics targeting distinct failure modes. WoRD is the only method that improves all four metrics jointly, including the safety-critical confident-and-wrong rate. WoRD runs under a single inference procedure and preserves calibrated multimodal. beliefs in complex, ambiguous environments where filter- and classifier-based observers collapse to a single mode or grow overconfident.

NeurIPS 2026

WILD: Widely Linear Conditioning for Time Series Forecasting

Binli Luo, Wanrong Ma, Ning Gui, Xianhan Tan

Transformer-based time series forecasting models often suffer from block-wise attention collapse, where temporal smoothness and cross-variable correlations concentrate attention locally and restrict global modeling capacity. We argue that this collapse is partly a pre-attention representation-conditioning problem: attention logits inherit the spectral concentration and low effective rank of the input representation. We propose Widely Linear Frequency-Domain (WILD) conditioning, a lightweight, model-agnostic module inserted before self-attention. WILD maps inputs to the frequency domain, applies data-dependent spectral preconditioning to redistribute over-dominant frequency energy, and then uses asymmetric real/imaginary projections to realize a widely linear transform beyond fixed time-domain channel mixing. The preconditioning step is essential: it constructs the usable normalized frequency basis on which the widely linear branch can operate. Thus, WILD uses frequency-domain modeling to condition an existing attention layer, not to replace it with a new forecasting architecture. Extensive experiments on eight benchmark datasets show positive gains on 105 of 112 model-dataset-metric configurations across seven backbones. Attention diagnostics show that WILD substantially increases effective rank over the baseline, and a W_r=W_i ablation identifies spectral preconditioning as the primary mechanism, with widely linear mixing providing a secondary, dataset-dependent gain.

NeurIPS 2026

WAXAL: A Large-Scale Multilingual African Language Speech Corpus

MohamedElfatih MohamedKhair, Emmanuel Asiedu Brempong, Subhashini Venugopalan, Abdoulaye Diack, Perry Nelson, Prince Mireku, Tavonga Siyavora, Pooja Rao, Uche Okonkwo, Angela Nakalembe, Abhishek Bapna, Aisha Walcott-Bryant

The advancement of speech technology has predominantly favored high-resource languages, creating a significant digital divide for speakers of most Sub-Saharan African languages. To address this gap, we introduce WAXAL, a large-scale, openly accessible speech dataset for 24 languages (spanning 19 for ASR and 13 for TTS, with overlaps) representing over 100 million speakers. The collection consists of an Automatic Speech Recognition (ASR) dataset containing approximately 2,340 hours of transcribed, image-prompted natural speech (over 14,100 hours of total collected audio) from a diverse range of speakers, and a Text-to-Speech (TTS) dataset with over 235 hours of high-quality, single-speaker studio recordings of phonetically balanced scripts. Crucially, this effort was executed in partnership with four African academic and community organizations, with the explicit goal of building the local ecosystem for speech technology and seeding data collection capabilities within these institutions. To demonstrate the dataset's utility, we benchmark three architecturally distinct ASR models---Gemma 3n-2B, Whisper-Large-v3, and MMS-1b-all---across the 19 ASR languages. Fine-tuning on WAXAL yields substantial improvements, reducing the macro-average Word Error Rate (WER) by up to 61\% (e.g., from 1.23 to 0.48 for Whisper). Models fine-tuned solely on WAXAL also generalize to the independently collected FLEURS benchmark, confirming the dataset's value for domain-transferable ASR adaptation. Furthermore, we employ an LLM-as-judge framework to evaluate semantic meaning preservation, demonstrating that fine-tuned predictions successfully capture core intents of native speakers. The WAXAL datasets are released at https://huggingface.co/datasets/google/WaxalNLP under the CC-BY-4.0 license to catalyze research and the development of inclusive speech technologies for speakers of African languages.

NeurIPS 2026

WASP: Weakly Aligned Spatiotemporal Pairs for Fetal Brain MRI-Ultrasound Learning

Francesco Correnti, Gabriele Magrini, Marco Mistretta, Niccolò Biondi, Pietro Pala, Alessandro Ramalli, simona fiori, Andrew Bagdanov, Matteo Lenge

Magnetic Resonance Imaging (MRI) is widely regarded as the optimal sensor for fetal brain analysis due to its superior soft tissue contrast and anatomical detail. However, its high cost and operational burden make it invasive and difficult to obtain at scale. Ultrasound (US), in contrast, is cheap, safe, and routinely acquired, and as a result it has produced substantially larger datasets and a growing ecosystem of pretrained models. This asymmetry raises a natural question: Can we teach a US-only model to understand fetal MRI from only a limited set of examples? The standard recipe, training a foundation model on subject-to-subject paired MRI-US scans, is not viable since no such paired fetal dataset is publicly available. In this paper we address this gap with Weakly Aligned Spatiotemporal Pairs (WASP), a framework that formulates cross-modal correspondence as an entropic Optimal Transport problem driven by clinical metadata — in particular, Gestational Age (GA) and diagnostic planes — enabling the fitting of a lightweight alignment head that lifts MRI representations into the US latent space, without fine-tuning the backbone. Empirically, WASP yields its largest gains when MRI is unseen by the model during pretraining (on USFM, GA estimation error drops from $21.9$ to $16.3$ days and standard plane classification accuracy climbs from 61.9\% to 74.5\%), while still providing refining improvements for backbones pretrained on both modalities (e.g., BioMedParse GA estimation error from $6.5$ to $5.6$ days and SAM-Med2d plane accuracy from $83.3$\% to $88.1$\%).

NeurIPS 2026

Voxel as Token: A New Perspective for Zero-shot Cross-subject Vision Decoding

Yulong Liu, Ziqiu Huang, Hua Xu, Guibo Zhu, Sirui Han, Yike Guo

Recent advances in brain decoding have achieved impressive visual reconstruction under subject-specific settings, yet they fail to generalize to unseen subjects without retraining---hindering practical zero-shot cross-subject applications. The core challenges stem from inter-subject variability in voxel dimensionality and misaligned spatial response patterns. While existing methods rely on surface-based alignment or complex feature disentanglement, they often operate as black boxes and overlook the potential of volume-based fMRI data. To address this, we propose \textbf{Voxel as Token (VoxTok)}, a conceptual framework that treats each fMRI voxel as an independent token endowed with a learnable functional embedding. This formulation naturally handles variable-length inputs and subsumes existing adapter-based models as special cases where linear projections approximate voxel functionality. Guided by the hypothesis that large-scale spatial distributions of neural activity are consistent across subjects despite fine-grained variability, we introduce a KNN-based estimator to predict functional embeddings for unseen subjects. This approach achieves state-of-the-art zero-shot retrieval performance and comparable reconstruction quality, while enabling plug-and-play adaptation for existing models (e.g., MindEye2). Integrating multi-scale ROIs further boosts performance, with our best model achieving $40.4\%$ zero-shot image retrieval accuracy, rivaling early supervised methods. Crucially, we find that decoding success correlates strongly with ROI size, indicating that global co-activation patterns drive cross-subject generalization.

NeurIPS 2026

Vortex: Efficient and Programmable Sparse Attention Serving

Zhuoming Chen, Xinrui Zhong, Qilong Feng, Ranajoy Sadhukhan, Yang Zhou, Michael Shieh, Zhihao Jia, Beidi Chen

Sparse attention is becoming increasingly important for serving large language models (LLMs) as generation lengths continue to grow. However, deploying and evaluating new sparse attention algorithms at scale remains highly engineering-intensive, slowing both human researchers and AI agents in exploring the sparse attention design. To address this challenge, we present Vortex, a system that combines a Python-embedded frontend language atop a page-centric tensor abstraction for expressing a broad range of sparse attention algorithms, with an efficient backend tightly integrated into modern LLM serving stacks. Vortex enables rapid prototyping, deployment, and evaluation of sparse attention algorithms, effectively translating their theoretical efficiency gains into real-world throughput improvements. As a result, Vortex substantially accelerates the design and iteration of sparse attention algorithms. Using Vortex, we further demonstrate AI-agent-driven exploration of the sparse attention, automatically generating and refining diverse algorithms that achieve strong accuracy-throughput trade-offs, with the best generated algorithms delivering up to $3.46\times$ higher throughput than full attention while preserving accuracy.

NeurIPS 2026

Voronoi-Markov chain and spatial entropy for point pattern analysis

James C Mathews, Francisco Couzo, Aleksandr Petrov, Avijit Chatterjee, Saad Nadeem

In this paper, we revisit the concept of entropy in the spatial context with the aim of deriving computable and interpretable metrics for point pattern analysis in domains such as histopathology. We discuss stochastic point process assumptions like Poisson homogeneity and Simple Sequential Inhibition (SSI) and review established results for Voronoi and Delaunay tilings of point sets for their potential to provide null distributions for rigorous empirical hypothesis testing. We present (1) a novel ``dense basin entropy'' defined in terms of the Ord distribution supported on Voronoi basins, which is shown to be sensitive to clustering, and (2) a related Markov chain designed as a simplification or approximation of Brownian motion in the underlying planar domain. We prove a lower bound on the dense basin entropy in the SSI regime (originally discovered in empirical experiments) and show that the entropy rate and spectral gap of the Markov chain lead to sharp discrimination metrics. Finally, we demonstrate the generalization to multiple-set analysis via aggregation of one set over the Markov invariant measure for another. Simulations and experiments in histopathology show that our proposed metrics offer insights complementary to other instantiations of entropy in spatial analysis.

NeurIPS 2026

Volatility-Whitened Probabilistic Residual Modeling for Long-Term Time Series Forecasting

Fan Zhang, Shiming Fan, Zexuan Ma, Shijun Chen, Meijia Wang, Hua Wang

Compared with deterministic methods that output only point estimates, probabilistic forecasting can characterize both future trends and their uncertainty simultaneously, making it more suitable for decision-making in complex real-world scenarios. In recent years, diffusion models, owing to their powerful generative modeling capability, have been introduced into the field of time series forecasting. However, we find that most existing diffusion-based forecasting methods directly construct the diffusion process in the original future space, which is easily affected by heteroscedastic scale imbalance, causing highly volatile dimensions to dominate the denoising learning and leading to unstable corrections near observation boundaries. Motivated by these issues, we propose VolaRM, a volatility-whitened probabilistic residual modeling framework for long-term time series forecasting. By constructing a conditional probabilistic base distribution, it represents future targets as whitened residuals relative to this base distribution and performs conditional modeling in the normalized residual space, thereby alleviating scale imbalance across variables and forecasting horizons. Meanwhile, a specific gating mechanism is introduced to enhance boundary continuity and the stability of long-term forecasting. Extensive experiments on eight real-world datasets from different application domains demonstrate the effectiveness of VolaRM.

NeurIPS 2026

VolFill: Single-View Amodal 3D Scene Reconstruction with Volumetric Flow Matching

Tuan Ngo, Chuang Gan, Evangelos Kalogerakis

Reconstructing the complete geometry of a scene from a single RGB image remains challenging—especially when inferring hidden structures where visual evidence is incomplete. We introduce VolFill, a generative framework that predicts the 3D structure of the complete scene rather than relying on traditional pixel-aligned regression. Our method utilizes a hybrid 3D VAE to compress sparse truncated unsigned distance function grids into a compact latent space, paired with a latent Diffusion Transformer that denoises this representation to recover the complete scene. We condition the generation on geometry foundation models, leveraging rich spatial priors for robust reasoning. Unlike existing methods limited by per-ray constraints or unstructured point-cloud queries, VolFill provides a structured representation that supports direct surface extraction and occupancy queries at scale. Extensive experiments on the 3D-FRONT and NRGBD datasets demonstrate that our approach significantly outperforms current baselines, providing a robust foundation for holistic spatial understanding.

NeurIPS 2026

VolCo: Volumetric Contact for High-Fidelity Human Grasp Generation

Zhuo Chen, Yihua Cheng, Ales Leonardis, Hyung Jin Chang

Accurate contact modeling is fundamental to understanding hand–object interaction, yet existing contact representations are typically restricted to object surfaces and rely on hand‑crafted rules to recover contact details, leading to severe penetrations and implausible results. To better exploit the rich detail in motion‑capture data, we introduce Volumetric Contact (VolCo), a representation that expands surface points to a set of 3D volumetric grids. VolCo encodes 3D contact that allows precise hand part recovery, and is organized in an inherent hierarchy: local contact details within each volume and global hand geometry across all volumes. Our framework, VolCoDiff, employs two modules to capture local and global features following this hierarchy. For local contact details, we use a 3D variational autoencoder to model the possible hand configurations conditioned on the local object signed distance field (SDF). For global hand geometry, we design a prior‑guided diffusion model that learns the distribution of compressed latent features aggregated from the volumetric grids. We evaluate our method on two benchmark datasets and demonstrate state‑of‑the‑art performance in penetration and stability, indicating the capability to generate tight grasps with much less severe penetrations.

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