NeurIPS 2025 Papers

We propose a generalized score-based diffusion framework for learning multivariate Gaussian mixture models with homoscedastic or heteroscedastic noise. Our goal is to nonparametrically estimate the latent location distribution and denoise the observations. Departing from the conventional maximum likelihood approach, we reinterpret each observation as a temporal slice of a family of stochastic diffusion processes. This modeling choice enables a principled characterization of the additive noise structure and supports a multi-step denoising procedure grounded in reverse-time dynamics. We introduce a score-based objective that explicitly models the latent distribution and accommodates observation-specific noise covariances. Theoretically, we establish that the score estimation error with $n$ independent observations achieves a near-parametric error rate of $\frac{\mathrm{polylog}(n)}{n}$, improving upon existing results in the diffusion literature. Empirically, our method outperforms the nonparametric maximum likelihood estimator in both density estimation and denoising fidelity, especially in high-dimensional settings. These findings suggest a promising direction for integrating nonparametric empirical Bayes with diffusion-based generative modeling for latent structure recovery.

Time series are often irregularly sampled with uneven time intervals. In multivariate cases, such irregularities may lead to misaligned observations across variables and varying observation counts, making it difficult to extract intrinsic patterns and degrading the classification performance of deep learning models. In this study, we propose an adaptive time encoding approach to address the challenge of irregular sampling in multivariate time-series classification. Our approach generates latent representations at learnable reference points that capture missingness patterns in irregular sequences, enhancing classification performance. We also introduce consistency regularization techniques to incorporate intricate temporal and intervariable information into the learned representations. Extensive experiments demonstrate that our method achieves state-of-the-art performance with high computational efficiency in irregular multivariate time-series classification tasks.

We investigate various stochastic bandit problems in the presence of adversarial corruptions. A seminal work for this problem is the BARBAR~\cite{gupta2019better} algorithm, which achieves both robustness and efficiency. However, it suffers from a regret of $O(KC)$, which does not match the lower bound of $\Omega(C)$, where $K$ denotes the number of arms and $C$ denotes the corruption level. In this paper, we first improve the BARBAR algorithm by proposing a novel framework called BARBAT, which eliminates the factor of $K$ to achieve an optimal regret bound up to a logarithmic factor. We also extend BARBAT to various settings, including multi-agent bandits, graph bandits, combinatorial semi-bandits and batched bandits. Compared with the Follow-the-Regularized-Leader framework, our methods are more amenable to parallelization, making them suitable for multi-agent and batched bandit settings, and they incur lower computational costs, particularly in semi-bandit problems. Numerical experiments verify the efficiency of the proposed methods.

In this paper, we introduce knowledge image generation as a new task, alongside the Massive Multi-Discipline Multi-Tier Knowledge-Image Generation Benchmark (MMMG) to probe the reasoning capability of image generation models. Knowledge images have been central to human civilization and to the mechanisms of human learning—a fact underscored by dual-coding theory and the picture-superiority effect. Generating such images is challenging, demanding multimodal reasoning that fuses world knowledge with pixel-level grounding into clear explanatory visuals. To enable comprehensive evaluation, MMMG offers $4,456$ expert-validated (knowledge) image-prompt pairs spanning $10$ disciplines, $6$ educational levels, and diverse knowledge formats such as charts, diagrams, and mind maps. To eliminate confounding complexity during evaluation, we adopt a unified Knowledge Graph (KG) representation. Each KG explicitly delineates a target image’s core entities and their dependencies. We further introduce MMMG-Score‌ to evaluate generated knowledge images. This metric combines factual fidelity, measured by graph-edit distance between KGs, with visual clarity assessment. Comprehensive evaluations of $21$ state-of-the-art text-to-image generation models expose serious reasoning deficits—low entity fidelity, weak relations, and clutter—with GPT-4o achieving an MMMG-Score‌ of only $50.20$, underscoring the benchmark’s difficulty. To spur further progress, we release FLUX-Reason (MMMG-Score‌ of $34.45$), an effective and open baseline that combines a reasoning LLM with diffusion models and is trained on $16,000$ curated knowledge image–prompt pairs.

Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result, they are fundamentally ill-suited for applications involving inherently discrete quantities such as particle counts or material units, that are constrained by strict conservation laws like mass conservation, limiting their applicability in scientific workflows. To address this limitation, we propose Discrete Spatial Diffusion (DSD), a framework based on a continuous-time, discrete-state jump stochastic process that operates directly in discrete spatial domains while strictly preserving particle counts in both forward and reverse diffusion processes. By using spatial diffusion to achieve particle conservation, we introduce stochasticity naturally through a discrete formulation. We demonstrate the expressive flexibility of DSD by performing image synthesis, class conditioning, and image inpainting across standard image benchmarks, while exactly conditioning total image intensity. We validate DSD on two challenging scientific applications: porous rock microstructures and lithium-ion battery electrodes, demonstrating its ability to generate structurally realistic samples under strict mass conservation constraints, with quantitative evaluation using state-of-the-art metrics for transport and electrochemical performance.

Understanding architectural differences in language models is challenging, especially at academic-scale pretraining (e.g., 1.3B parameters, 100B tokens), where results are often dominated by noise and randomness. To overcome this, we introduce controlled synthetic pretraining tasks that isolate and evaluate core model capabilities. Within this framework, we discover \emph{Canon layers}: lightweight architectural components—named after the musical term ``canon''—that promote horizontal information flow across neighboring tokens. Canon layers compute weighted sums of nearby token representations and integrate seamlessly into Transformers, linear attention, state-space models, or any sequence architecture. We present 12 key results. This includes how Canon layers enhance reasoning depth (e.g., by $2\times$), reasoning breadth, knowledge manipulation, etc. They lift weak architectures like NoPE to match RoPE, and linear attention to rival SOTA linear models like Mamba2/GDN—validated both through synthetic tasks and real-world academic-scale pretraining. This synthetic playground offers an \emph{economical, principled path} to isolate core model capabilities often obscured at academic scales. Equipped with infinite high-quality data, it may even \emph{predict} how future architectures will behave as training pipelines improve—e.g., through better data curation or RL-based post-training—unlocking deeper reasoning and hierarchical inference.

Graph Neural Networks (GNNs) are increasingly deployed in mission-critical tasks, yet they often encounter inputs that lie outside their training distribution, leading to unreliable or overconfident predictions. To address this limitation, we present RAGNOR (Robust Aggregation Graph Norm for Outlier Recognition), a post-hoc approach that leverages embedding norms for robust out-of-distribution (OOD) detection on both node-level and graph-level tasks. Unlike previous methods designed primarily for image domains, RAGNOR directly tackles the relational challenges intrinsic to graphs: local contamination by anomalous neighbors, disparate norm scales across classes or roles, and insufficient references for boundary or low-degree nodes. By combining global Z-score normalization, median-based local aggregation, and multi-hop blending, RAGNOR effectively refines raw norm signals into robust OOD scores while incurring minimal overhead and requiring no retraining of the original GNN. Experimental evaluations on multiple benchmarks demonstrate that RAGNOR not only achieves competitive or superior detection performance compared to alternative techniques, but also provides an intuitive, modular design that can be readily integrated into existing graph pipelines.

The increasing use of 360$^\circ$ images across various domains has emphasized the need for robust depth estimation techniques tailored for omnidirectional images. However, obtaining large-scale labeled datasets for 360$^\circ$ depth estimation remains a significant challenge. In this paper, we propose RPG360, a training-free robust 360$^\circ$ monocular depth estimation method that leverages perspective foundation models and graph optimization. Our approach converts 360$^\circ$ images into six- face cubemap representations, where a perspective foundation model is employed to estimate depth and surface normals. To address depth scale inconsistencies across different faces of the cubemap, we introduce a novel depth scale alignment technique using graph-based optimization, which parameterizes the predicted depth and normal maps while incorporating an additional per-face scale parameter. This optimization ensures depth scale consistency across the six-face cubemap while preserving 3D structural integrity. Furthermore, as foundation models exhibit inherent robustness in zero-shot settings, our method achieves superior performance across diverse datasets, including Matterport3D, Stanford2D3D, and 360Loc. We also demonstrate the versatility of our depth estimation approach by validating its benefits in downstream tasks such as feature matching 3.2 ∼ 5.4% and Structure from Motion 0.2 ∼ 9.7% in AUC@5$^\circ$.

We propose Equivariance by Contrast (EbC) to learn equivariant embeddings from observation pairs $(\mathbf{y}, g \cdot \mathbf{y})$, where $g$ is drawn from a finite group acting on the data. Our method jointly learns a latent space and a group representation in which group actions correspond to invertible linear maps—without relying on group-specific inductive biases. We validate our approach on the infinite dSprites dataset with structured transformations defined by the finite group $G:= (R_m \times \mathbb{Z}_n \times \mathbb{Z}_n)$, combining discrete rotations and periodic translations. The resulting embeddings exhibit high-fidelity equivariance, with group operations faithfully reproduced in latent space. On synthetic data, we further validate the approach on the non-abelian orthogonal group $O(n)$ and the general linear group $GL(n)$. We also provide a theoretical proof for identifiability. While broad evaluation across diverse group types on real-world data remains future work, our results constitute the first successful demonstration of general-purpose encoder-only equivariant learning from group action observations alone, including non-trivial non-abelian groups and a product group motivated by modeling affine equivariances in computer vision.

We demonstrate, for the first time, fully quantized training (FQT) of large language models (LLMs) using predominantly 4-bit floating-point (FP4) precision for weights, activations, and gradients on datasets up to 200 billion tokens. We extensively investigate key design choices for FP4, including block sizes, scaling formats, and rounding methods. Our analysis shows that the NVFP4 format, where each block of 16 FP4 values (E2M1) shares a scale represented in E4M3, provides optimal results. We use stochastic rounding for backward and update passes and round-to-nearest for the forward pass to enhance stability. Additionally, we identify a theoretical and empirical threshold for effective quantized training: when the gradient norm falls below approximately $\sqrt{3}$ times the quantization noise, quantized training becomes less effective. Leveraging these insights, we successfully train a 7-billion-parameter model on 256 Intel Gaudi2 accelerators. The resulting FP4-trained model achieves downstream task performance comparable to a standard BF16 baseline, confirming that FP4 training is a practical and highly efficient approach for large-scale LLM training. A reference implementation is supplied in https://github.com/Anonymous1252022/fp4-all-the-way.

To migrate the remarkable successes of Large Language Models (LLMs), the community has made numerous efforts to generalize them to the table reasoning tasks for the widely deployed tabular data. Despite that, in this work, by showing a probing experiment on our proposed StructQA benchmark, we postulate that even the most advanced LLMs (such as GPTs) may still fall short of coping with tabular data. More specifically, the current scheme often simply relies on serializing the tabular data, together with the meta information, then inputting them through the LLMs. We argue that the loss of structural information is the root of this shortcoming. In this work, we further propose TAMO, which bears an ideology to treat the tables as an independent modality integrated with the text tokens. The resulting model in TAMO is a multimodal framework consisting of a hypergraph neural network as the global table encoder seamlessly integrated with the mainstream LLM. Empirical results on various benchmarking datasets, including HiTab, WikiTQ, WikiSQL, FeTaQA, and StructQA, have demonstrated significant improvements on generalization with an average relative gain of **42.65%**.

Large language models (LLMs) excel in tasks like question answering and dialogue, but complex tasks requiring interaction, such as negotiation and persuasion, require additional long-horizon reasoning and planning. Reinforcement learning (RL) fine-tuning can enable such planning in principle, but suffers from drawbacks that hinder scalability. In particular, multi-turn RL training incurs high memory and computational costs, which are exacerbated when training LLMs as policies. Furthermore, the largest LLMs do not expose the APIs necessary to be trained in such manner. As a result, modern methods to improve the reasoning of LLMs rely on sophisticated prompting mechanisms rather than RL fine-tuning. To remedy this, we propose a novel approach that uses goal-conditioned value functions to guide the reasoning of LLM agents, that scales even to large API-based models. These value functions predict how a task will unfold given an action, allowing the LLM agent to evaluate multiple possible outcomes, both positive and negative, to plan effectively. In addition, these value functions are trained over reasoning steps rather than full actions, to be a concise and light-weight module that facilitates decision-making in multi-turn interactions. We validate our method on tasks requiring interaction, including tool use, social deduction, and dialogue, demonstrating superior performance over both RL fine-tuning and prompting methods while maintaining efficiency and scalability.

The task of localizing an object's spatial tube based on language instructions and video, known as spatial video grounding (SVG), has attracted widespread interest. Existing SVG tasks have focused on ego-centric fixed front perspective and simple scenes, which only involved a very limited view and environment. However, UAV-based SVG remains underexplored, which neglects the inherent disparities in drone movement and the complexity of aerial object localization. To facilitate research in this field, we introduce the novel spatial aerial video grounding (SAVG) task. Specifically, we meticulously construct a large-scale benchmark, UAV-SVG, which contains over 2 million frames and offers 216 highly diverse target categories. To address the disparities and challenges posed by complex aerial environments, we propose a new end-to-end transformer architecture, coined SAVG-DETR. The innovations are three-fold. 1) To overcome the computational explosion of self-attention when introducing multi-scale features, our encoder efficiently decouples the multi-modality and multi-scale spatio-temporal modeling into intra-scale multi-modality interaction and cross-scale visual-only fusion. 2) To enhance small object grounding ability, we propose the language modulation module to integrate multi-scale information into language features and the multi-level progressive spatial decoder to decode from high to low level. The decoding stage for the lower-level vision-language features is gradually increased. 3) To improve the prediction consistency across frames, we design the decoding paradigm based on offset generation. At each decoding stage, we utilize reference anchors to constrict the grounding region, use context-rich object queries to predict offsets, and update reference anchors for the next stage. From coarse to fine, our SAVG-DETR gradually bridges the modality gap and iteratively refines reference anchors of the referred object, eventually grounding the spatial tube. Extensive experiments demonstrate that our SAVG-DETR significantly outperforms existing state-of-the-art methods. The dataset and code will be available at here.

Dual encoder (DE) models, where a pair of matching query and document are embedded into similar vector representations, are widely used in information retrieval due to their simplicity and scalability. However, the Euclidean geometry of the embedding space limits the expressive power of DEs, which may compromise their quality. This paper investigates such limitations in the context of hierarchical retrieval (HR), where the document set has a hierarchical structure and the matching documents for a query are all of its ancestors. We first prove that DEs are feasible for HR as long as the embedding dimension is linear in the depth of the hierarchy and logarithmic in the number of documents. Then we study the problem of learning such embeddings in a standard retrieval setup where DEs are trained on samples of matching query and document pairs. Our experiments reveal a lost-in-the-long-distance phenomenon, where retrieval accuracy degrades for documents further away in the hierarchy. To address this, we introduce a pretrain-finetune recipe that significantly improves long-distance retrieval without sacrificing performance on closer documents. We experiment on a realistic hierarchy from WordNet for retrieving documents at various levels of abstraction, and show that pretrain-finetune boosts the recall on long-distance pairs from 19% to 76%. Finally, we demonstrate that our method improves retrieval of relevant products on a shopping queries dataset.

We introduce AutoJudge, a method that accelerates large language model (LLM) inference with task-specific lossy speculative decoding. Instead of matching the original model output distribution token-by-token, we identify the generated tokens that affect the downstream quality of the response, relaxing the distribution match guarantee so that the "unimportant" tokens can be generated faster. Our approach relies on a semi‑greedy search algorithm to test which of the mismatches between target and draft models should be corrected to preserve quality and which ones may be skipped. We then train a lightweight classifier based on existing LLM embeddings to predict, at inference time, which mismatching tokens can be safely accepted without compromising the final answer quality. We evaluate AutoJudge with multiple draft/target model pairs on mathematical reasoning and programming benchmarks, achieving significant speedups at the cost of a minor accuracy reduction. Notably, on GSM8K with the Llama 3.1 70B target model, our approach achieves up to ${\approx}2{\times}$ speedup \textit{over speculative decoding} at the cost of a ${\le} 1\%$ drop in accuracy. When applied to the LiveCodeBench benchmark, AutoJudge automatically detects programming-specific important tokens, accepting ${\ge}25$ tokens per speculation cycle at a$~ 2\%$ drop in Pass@1. Our approach requires no human annotation and is easy to integrate with modern LLM inference frameworks.

Multimodal large language models (MLLMs) remain vulnerable to transferable adversarial examples. While existing methods typically achieve targeted attacks by aligning global features—such as CLIP’s [CLS] token—between adversarial and target samples, they often overlook the rich local information encoded in patch tokens. This leads to suboptimal alignment and limited transferability, particularly for closed-source models. To address this limitation, we propose a targeted transferable adversarial attack method based on feature optimal alignment, called FOA-Attack, to improve adversarial transfer capability. Specifically, at the global level, we introduce a global feature loss based on cosine similarity to align the coarse-grained features of adversarial samples with those of target samples. At the local level, given the rich local representations within Transformers, we leverage clustering techniques to extract compact local patterns to alleviate redundant local features. We then formulate local feature alignment between adversarial and target samples as an optimal transport (OT) problem and propose a local clustering optimal transport loss to refine fine-grained feature alignment. Additionally, we propose a dynamic ensemble model weighting strategy to adaptively balance the influence of multiple models during adversarial example generation, thereby further improving transferability. Extensive experiments across various models demonstrate the superiority of the proposed method, outperforming state-of-the-art methods, especially in transferring to closed-source MLLMs.

We study offline imitation learning (IL) in cooperative multi-agent settings, where demonstrations have unlabeled mixed quality - containing both expert and suboptimal trajectories. Our proposed solution is structured in two stages: trajectory labeling and multi-agent imitation learning, designed jointly to enable effective learning from heterogeneous, unlabeled data. In the first stage, we combine advances in large language models and preference-based reinforcement learning to construct a progressive labeling pipeline that distinguishes expert-quality trajectories. In the second stage, we introduce MisoDICE, a novel multi-agent IL algorithm that leverages these labels to learn robust policies while addressing the computational complexity of large joint state-action spaces. By extending the popular single-agent DICE framework to multi-agent settings with a new value decomposition and mixing architecture, our method yields a convex policy optimization objective and ensures consistency between global and local policies. We evaluate MisoDICE on multiple standard multi-agent RL benchmarks and demonstrate superior performance, especially when expert data is scarce.

Rectified flow is a generative model that learns smooth transport mappings between two distributions through an ordinary differential equation (ODE). The model learns a straight ODE by reflow steps which iteratively update the supervisory flow. It allows for a relatively simple and efficient generation of high-quality images. However, rectified flow still faces several challenges. 1) The reflow process is slow because it requires a large number of generated pairs to model the target distribution. 2) It is well known that the use of suboptimal fake samples in reflow can lead to performance degradation of the learned flow model. This issue is further exacerbated by error accumulation across reflow steps and model collapse in denoising autoencoder models caused by self-consuming training. In this work, we go one step further and empirically demonstrate that the reflow process causes the learned model to drift away from the target distribution, which in turn leads to a growing discrepancy in reconstruction error between fake and real images. We reveal the drift problem and design a new reflow step, namely the conic reflow. It supervises the model by the inversions of real data points through the previously learned model and its interpolation with random initial points. Our conic reflow leads to multiple advantages. 1) It keeps the ODE paths toward real samples, evaluated by reconstruction. 2) We use only a small number of generated samples instead of large generated samples, 600K and 4M, respectively. 3) The learned model generates images with higher quality evaluated by FID, IS, and Recall. 4) The learned flow is more straight than others, evaluated by curvature. We achieve much lower FID in both one-step and full-step generation in CIFAR-10. The conic reflow generalizes to various datasets such as LSUN Bedroom and ImageNet.

Contrastive Language-Image Pre-training (CLIP) has become a foundation model and has been applied to various vision and multimodal tasks. However, recent works indicate that CLIP falls short in distinguishing detailed differences in images and shows suboptimal performance on dense-prediction and vision-centric multimodal tasks. Therefore, this work focuses on improving existing CLIP models, aiming to capture as many visual details in images as possible. We find that a specific type of generative models, unCLIP, provides a suitable framework for achieving our goal. Specifically, unCLIP trains an image generator conditioned on the CLIP image embedding. In other words, it inverts the CLIP image encoder. Compared to discriminative models like CLIP, generative models are better at capturing image details because they are trained to learn the data distribution of images. Additionally, the conditional input space of unCLIP aligns with CLIP's original image-text embedding space. Therefore, we propose to invert unCLIP (dubbed un$^2$CLIP) to improve the CLIP model. In this way, the improved image encoder can gain unCLIP's visual detail capturing ability while preserving its alignment with the original text encoder simultaneously. We evaluate our improved CLIP across various tasks to which CLIP has been applied, including the challenging MMVP-VLM benchmark, the dense-prediction open-vocabulary segmentation task, and multimodal large language model tasks. Experiments show that un$^2$CLIP significantly improves the original CLIP and previous CLIP improvement methods. Code and models are available at https://github.com/LiYinqi/un2CLIP.