NeurIPS 2025 Papers

Conditional sampling is a fundamental task in Bayesian statistics and generative modeling. Consider the problem of sampling from the posterior distribution $P\_{X|Y=y^\*}$ for some observation $y^\*$, where the likelihood $P\_{Y|X}$ is known, and we are given $n$ i.i.d. samples $D=\\{X\_i\\}\_{i=1}^n$ drawn from an unknown prior distribution $\pi\_X$. Suppose that $f(\hat{\pi}\_{X^n})$ is the distribution of a posterior sample generated by an algorithm (e.g. a conditional generative model or the Bayes rule) when $\hat{\pi}\_{X^n}$ is the empirical distribution of the training data. Although averaging over the randomness of the training data $D$, we have $\mathbb{E}\_D\left(\hat{\pi}\_{X^n}\right)= \pi\_X$, we do not have $\mathbb{E}\_D\left\\{f(\hat{\pi}\_{X^n})\right\\}= f(\pi\_X)$ due to the nonlinearity of $f$, leading to a bias. In this paper we propose a black-box debiasing scheme that improves the accuracy of such a naive plug-in approach. For any integer $k$ and under boundedness of the likelihood and smoothness of $f$, we generate samples $\hat{X}^{(1)},\dots,\hat{X}^{(k)}$ and weights $w\_1,\dots,w\_k$ such that $\sum_{i=1}^kw_iP\_{\hat{X}^{(i)}}$ is a $k$-th order approximation of $f(\pi\_X)$, where the generation process treats $f$ as a black-box. Our generation process achieves higher accuracy when averaged over the randomness of the training data, without degrading the variance, which can be interpreted as improving memorization without compromising generalization in generative models.

Probabilistic time series forecasting, essential in domains like healthcare and neuroscience, requires models capable of capturing uncertainty and intricate temporal dependencies. While deep learning has advanced forecasting, generating calibrated probability distributions over continuous future values remains challenging. We introduce Temporal Generative Flow Networks (Temporal GFNs), adapting Generative Flow Networks (GFNs) – a powerful framework for generating compositional objects – to this sequential prediction task. GFNs learn policies to construct objects (eg. forecast trajectories) step-by-step, sampling final objects proportionally to a reward signal. However, applying GFNs directly to continuous time series necessitates addressing their inherently discrete action spaces and ensuring differentiability. Our framework tackles this by representing time series segments as states and sequentially generating future values via quantized actions chosen by a forward policy. We introduce two key innovations: (1) An adaptive, curriculum-based quantization strategy that dynamically adjusts the number of discretization bins based on reward improvement and policy entropy, balancing precision and exploration throughout training. (2) A straight-through estimator mechanism enabling the forward policy to output both discrete (hard) samples for trajectory construction and continuous (soft) samples for stable gradient propagation. Training utilizes a trajectory balance loss objective, ensuring flow consistency, augmented by an entropy regularizer. We provide rigorous theoretical bounds on the quantization error's impact and the adaptive factor's range. We demonstrate how Temporal GFNs offer a principled way to leverage the structured generation capabilities of GFNs for probabilistic forecasting in continuous domains.

We present MGE-LDM, a unified latent diffusion framework for simultaneous music generation, source imputation, and query-driven source separation. Unlike prior approaches constrained to fixed instrument classes, MGE-LDM learns a joint distribution over full mixtures, submixtures, and individual stems within a single compact latent diffusion model. At inference, MGE-LDM enables (1) complete mixture generation, (2) partial generation (i.e., source imputation), and (3) text-conditioned extraction of arbitrary sources. By formulating both separation and imputation as conditional inpainting tasks in the latent space, our approach supports flexible, class-agnostic manipulation of arbitrary instrument sources. Notably, MGE-LDM can be trained jointly across heterogeneous multi-track datasets (e.g., Slakh2100, MUSDB18, MoisesDB) without relying on predefined instrument categories.

We propose MoGe-2, an advanced open-domain geometry estimation model that recovers a metric-scale 3D point map of a scene from a single image. Our method builds upon the recent monocular geometry estimation approach, MoGe, which predicts affine-invariant point maps with unknown scales. We explore effective strategies to extend MoGe for metric geometry prediction without compromising the relative geometry accuracy provided by the affine-invariant point representation. Additionally, we discover that noise and errors in real data diminish fine-grained detail in the predicted geometry. We address this by developing a data refinement approach that filters and completes real data using sharp synthetic labels, significantly enhancing the granularity of the reconstructed geometry while maintaining the overall accuracy. We train our model on a large corpus of mixed datasets and conducted comprehensive evaluations, demonstrating its superior performance in achieving accurate relative geometry, precise metric scale, and fine-grained detail recovery -- capabilities that no previous methods have simultaneously achieved.

This paper investigates the limitations of the normalization in attention mechanisms. We begin with a theoretical framework that enables the identification of the model's selective ability and the geometric separation involved in token selection. Our analysis includes explicit bounds on distances and separation criteria for token vectors under softmax scaling. Through experiments with pre-trained GPT-2 model, we empirically validate our theoretical results and analyze key behaviors of the attention mechanism. Notably, we demonstrate that as the number of selected tokens increases, the model's ability to distinguish informative tokens declines, often converging toward a uniform selection pattern. We also show that gradient sensitivity under softmax normalization presents challenges during training, especially at low temperature settings. These findings advance current understanding of softmax-based attention mechanism and motivate the need for more robust normalization and selection strategies in future attention architectures.

Cultural awareness in language models is the capacity to understand and adapt to diverse cultural contexts. However, most existing approaches treat culture as static background knowledge, overlooking its dynamic and evolving nature. This limitation reduces their reliability in downstream tasks that demand genuine cultural sensitivity. In this work, we introduce CALM, a novel framework designed to endow language models with cultural self-awareness. CALM disentangles task semantics from explicit cultural concepts and latent cultural signals, shaping them into structured cultural clusters through contrastive learning. These clusters are then aligned via cross-attention to establish fine-grained interactions among related cultural features and are adaptively integrated through a Mixture-of-Experts mechanism along culture-specific dimensions. The resulting unified representation is fused with the model's original knowledge to construct a culturally grounded internal identity state, which is further enhanced through self-prompted reflective learning, enabling continual adaptation and self-correction. Experiments on the benchmark datasets demonstrate that CALM outperforms state-of-the-art methods.

Federated continual learning (FCL) has garnered increasing attention for its ability to support distributed computation in environments with evolving data distributions. However, the emergence of new tasks introduces both temporal and cross-client shifts, making catastrophic forgetting a critical challenge. Most existing works aggregate knowledge from clients into a global model, which may not enhance client performance since irrelevant knowledge could introduce interference, especially in heterogeneous scenarios. Additionally, directly applying decentralized approaches to FCL suffers from ineffective group formation caused by task changes. To address these challenges, we propose a decentralized dynamic cooperation framework for FCL, where clients establish dynamic cooperative learning coalitions to balance the acquisition of new knowledge and the retention of prior learning, thereby obtaining personalized models. To maximize model performance, each client engages in selective cooperation, dynamically allying with others who offer meaningful performance gains. This results in non-overlapping, variable coalitions at each stage of the task. Moreover, we use coalitional affinity game to simulate coalition relationships between clients. By assessing both client gradient coherence and model similarity, we quantify the client benefits derived from cooperation. We also propose a merge-blocking algorithm and a dynamic cooperative evolution algorithm to achieve cooperative and dynamic equilibrium. Comprehensive experiments demonstrate the superiority of our method compared to various baselines. Code is available at: https://github.com/ydn3229/DCFCL.

Imputation methods play a critical role in enhancing the quality of practical time-series data, which often suffer from pervasive missing values. Recently, diffusion-based generative imputation methods have demonstrated remarkable success compared to autoregressive and conventional statistical approaches. Despite their empirical success, the theoretical understanding of how well diffusion-based models capture complex spatial and temporal dependencies between the missing values and observed ones remains limited. Our work addresses this gap by investigating the statistical efficiency of conditional diffusion transformers for imputation and quantifying the uncertainty in missing values. Specifically, we derive statistical sample complexity bounds based on a novel approximation theory for conditional score functions using transformers, and, through this, construct tight confidence regions for missing values. Our findings also reveal that the efficiency and accuracy of imputation are significantly influenced by the missing patterns. Furthermore, we validate these theoretical insights through simulation and propose a mixed-masking training strategy to enhance the imputation performance.

Stochastic optimal control methods often struggle in complex non-convex landscapes, frequently becoming trapped in local optima due to their inability to learn from historical trajectory data. This paper introduces Memory-Augmented Potential Field Theory, a unified mathematical framework that integrates historical experience into stochastic optimal control. Our approach dynamically constructs memory-based potential fields that identify and encode key topological features of the state space, enabling controllers to automatically learn from past experiences and adapt their optimization strategy. We provide a theoretical analysis showing that memory-augmented potential fields possess non-convex escape properties, asymptotic convergence characteristics, and computational efficiency. We implement this theoretical framework in a Memory-Augmented Model Predictive Path Integral (MPPI) controller that demonstrates significantly improved performance in challenging non-convex environments. The framework represents a generalizable approach to experience-based learning within control systems (especially robotic dynamics), enhancing their ability to navigate complex state spaces without requiring specialized domain knowledge or extensive offline training.

In the pursuit of finding an optimal policy, reinforcement learning (RL) methods generally ignore the properties of learned policies apart from their expected return. Thus, even when successful, it is difficult to characterize which policies will be learned and what they will do. In this work, we present a theoretical framework for policy optimization that guarantees convergence to a particular optimal policy, via vanishing entropy regularization and a *temperature decoupling gambit*. Our approach realizes an interpretable, diversity-preserving optimal policy as the regularization temperature vanishes and ensures the convergence of policy derived objects--value functions and return distributions. In a particular instance of our method, for example, the realized policy samples all optimal actions uniformly. Leveraging our temperature decoupling gambit, we present an algorithm that estimates, to arbitrary accuracy, the return distribution associated to its interpretable, diversity-preserving optimal policy.

Gene regulatory network inference (GRNI) aims to discover how genes causally regulate each other from gene expression data. It is well-known that statistical dependencies in observed data do not necessarily imply causation, as spurious dependencies may arise from *latent confounders*, such as non-coding RNAs. Numerous GRNI methods have thus been proposed to address this confounding issue. However, dependencies may also result from *selection*—only cells satisfying certain survival or inclusion criteria are observed—while these selection-induced spurious dependencies are frequently overlooked in gene expression data analyses. In this work, we show that such selection is ubiquitous and, when ignored or conflated with true regulations, can lead to flawed causal interpretation and misguided intervention recommendations. To address this challenge, a fundamental question arises: can we distinguish dependencies due to regulation, confounding, and crucially, selection? We show that gene perturbations offer a simple yet effective answer: selection-induced dependencies are *symmetric* under perturbation, while those from regulation or confounding are not. Building on this motivation, we propose GISL (Gene regulatory network Inference in the presence of Selection bias and Latent confounders), a principled algorithm that leverages perturbation data to uncover both true gene regulatory relations and non-regulatory mechanisms of selection and confounding up to the equivalence class. Experiments on synthetic and real-world gene expression data demonstrate the effectiveness of our method.

A major challenge in using diffusion models is aligning outputs with user-defined conditions. Existing conditional generation methods fall into two major categories: classifier-based guidance, which requires differentiable target models and gradient-based correction; and classifier-free guidance, which embeds conditions directly into the diffusion model but demands expensive joint training and architectural coupling. In this work, we introduce a third paradigm: DISCrete nOise (DISCO) guidance, which replaces the continuous conditional correction term with a finite codebook of discrete noise vectors sampled from a Gaussian prior. Conditional generation is reformulated as a code selection task, and we train prediction network to choose the optimal code given the intermediate diffusion state and the conditioning input. Our approach is differentiability-free, and training-efficient, avoiding the gradient computation and architectural redundancy of prior methods. Empirical results demonstrate that DISCO achieves competitive controllability while substantially reducing resource demands, positioning it as a scalable and effective alternative for conditional diffusion generation.

Addressing the critical need for robust safety in Large Language Models (LLMs), particularly against adversarial attacks and in-distribution errors, we introduce Reinforcement Learning with Backtracking Feedback (RLBF). This framework advances upon prior methods, such as BSAFE, by primarily leveraging a Reinforcement Learning (RL) stage where models learn to dynamically correct their own generation errors. Through RL with critic feedback on the model's live outputs, LLMs are trained to identify and recover from their actual, emergent safety violations by emitting an efficient "backtrack by x tokens" signal, then continuing generation autoregressively. This RL process is crucial for instilling resilience against sophisticated adversarial strategies, including middle filling, Greedy Coordinate Gradient (GCG) attacks, and decoding parameter manipulations. To further support the acquisition of this backtracking capability, we also propose an enhanced Supervised Fine-Tuning (SFT) data generation strategy (BSAFE+). This method improves upon previous data creation techniques by injecting violations into coherent, originally safe text, providing more effective initial training for the backtracking mechanism. Comprehensive empirical evaluations demonstrate that RLBF significantly reduces attack success rates across diverse benchmarks and model scales, achieving superior safety outcomes while critically preserving foundational model utility.

Diffusion models show promise for dynamic scene deblurring; however, existing studies often fail to leverage the intrinsic nature of the blurring process within diffusion models, limiting their full potential. To address it, we present a Blur Diffusion Model (BlurDM), which seamlessly integrates the blur formation process into diffusion for image deblurring. Observing that motion blur stems from continuous exposure, BlurDM implicitly models the blur formation process through a dual-diffusion forward scheme, diffusing both noise and blur onto a sharp image. During the reverse generation process, we derive a dual denoising and deblurring formulation, enabling BlurDM to recover the sharp image by simultaneously denoising and deblurring, given pure Gaussian noise conditioned on the blurred image as input. Additionally, to efficiently integrate BlurDM into deblurring networks, we perform BlurDM in the latent space, forming a flexible prior generation network for deblurring. Extensive experiments demonstrate that BlurDM significantly and consistently enhances existing deblurring methods on four benchmark datasets. The source code is available at https://github.com/Jin-Ting-He/BlurDM.

Domain generalization aims to train models that perform robustly on unseen target domains without access to target data. The realm of vision-language foundation model has opened a new venue owing to its inherent out-of-distribution generalization capability. However, the static alignment to class-level textual anchors remains insufficient to handle the dramatic distribution discrepancy from diverse domain-specific visual features. In this work, we propose a novel cross-domain Schrödinger Bridge (SB) method, namely SBGen, to handle this challenge, which explicitly formulates the stochastic semantic evolution, to gain better generalization to unseen domains. Technically, the proposed \texttt{SBGen} consists of three key components: (1) \emph{text-guided domain-aware feature selection} to isolate semantically aligned image tokens; (2) \emph{stochastic cross-domain evolution} to simulate the SB dynamics via a learnable time-conditioned drift; and (3) \emph{stochastic domain-agnostic interpolation} to construct semantically grounded feature trajectories. Empirically, \texttt{SBGen} achieves state-of-the-art performance on domain generalization in both classification and segmentation. This work highlights the importance of modeling domain shifts as structured stochastic processes grounded in semantic alignment.

Accurate polyp sizing during endoscopy is crucial for cancer risk assessment but is hindered by subjective methods and inadequate datasets lacking integrated 2D appearance, 3D structure, and real-world size information. We introduce PolypSense3D, the first multi-source benchmark dataset specifically targeting depth-aware polyp size measurement. It uniquely integrates over 43,000 frames from virtual simulations, physical phantoms, and clinical sequences, providing synchronized RGB, dense/sparse depth, segmentation masks, camera parameters, and millimeter-scale size labels derived via a novel forceps-assisted in-vivo annotation technique. To establish its value, we benchmark state-of-the-art segmentation and depth estimation models. Results quantify significant domain gaps between simulated/phantom and clinical data and reveal substantial error propagation from perception stages to final size estimation, with the best fully automated pipelines achieving an average Mean Absolute Error (MAE) of 0.95 mm on the clinical data subset. Publicly released under CC BY-SA 4.0 with code and evaluation protocols, PolypSense3D offers a standardized platform to accelerate research in robust, clinically relevant quantitative endoscopic vision. The benchmark dataset and code are available at: https://github.com/HNUicda/PolypSense3D and https://doi.org/10.7910/DVN/K13H89.

Audio is inherently temporal and closely synchronized with the visual world, making it a naturally aligned and expressive control signal for controllable video generation (e.g., movies). Beyond control, directly translating audio into video is essential for understanding and visualizing rich audio narratives (e.g., Podcasts or historical recordings). However, existing approaches fall short in generating high-quality videos with precise audio-visual synchronization, especially across diverse and complex audio types. In this work, we introduce MTV, a versatile framework for audio-sync video generation. MTV explicitly separates audios into speech, effects, and music tracks, enabling disentangled control over lip motion, event timing, and visual mood, respectively—resulting in fine-grained and semantically aligned video generation. To support the framework, we additionally present DEMIX, a dataset comprising high-quality cinematic videos and demixed audio tracks. DEMIX is structured into five overlapped subsets, enabling scalable multi-stage training for diverse generation scenarios. Extensive experiments demonstrate that MTV achieves state-of-the-art performance across six standard metrics spanning video quality, text-video consistency, and audio-video alignment.

Large language models (LLMs) are increasingly used in learning algorithms, evaluations, and optimization tasks. Recent studies have shown that using LLM-based optimizers to automatically optimize model prompts, demonstrations, predictions themselves, or other components can significantly enhance the performance of AI systems, as demonstrated by frameworks such as DSPy and TextGrad. However, optimizers built on language models themselves are usually designed by humans with manual design choices; optimizers themselves are not optimized. Moreover, these optimizers are general purpose by design, to be useful to a broad audience, and are not tailored for specific tasks. To address these challenges, we propose metaTextGrad, which focuses on designing a meta-optimizer to further enhance existing optimizers and align them to be good optimizers for a given task. Our approach consists of two key components: a meta prompt optimizer and a meta structure optimizer. The combination of these two significantly improves performance across multiple benchmarks, achieving an average absolute performance improvement of up to 6% compared to the best baseline.

Local geometry-controllable computer-aided design (CAD) generation aims to modify local parts of CAD models automatically, enhancing design efficiency. It also ensures that the shapes of newly generated local parts follow user-specific geometric instructions (e.g., an isosceles right triangle or a rectangle with one corner cut off). However, existing methods encounter challenges in achieving this goal. Specifically, they either lack the ability to follow textual instructions or are unable to focus on the local parts. To address this limitation, we introduce GeoCAD, a user-friendly and local geometry-controllable CAD generation method. Specifically, we first propose a complementary captioning strategy to generate geometric instructions for local parts. This strategy involves vertex-based and VLLM-based captioning for systematically annotating simple and complex parts, respectively. In this way, we caption $\sim$221k different local parts in total. In the training stage, given a CAD model, we randomly mask a local part. Then, using its geometric instruction and the remaining parts as input, we prompt large language models (LLMs) to predict the masked part. During inference, users can specify any local part for modification while adhering to a variety of predefined geometric instructions. Extensive experiments demonstrate the effectiveness of GeoCAD in generation quality, validity and text-to-CAD consistency.