ICML 2026 论文列表

Origin–destination (OD) flow modeling underpins urban planning and mobility analysis, but prevailing graph-based methods often neglect salient geographic attributes, limiting their ability to model long-range and multi-area dependencies. In this paper, we introduce GeoFlow, a novel framework that (i) augments area representations with geospatial attributes, including relative positions, -hop and geodesic distances, (ii) employs a specialized geometric-intrinsic fusion encoder design that combines graph attention for intrinsic area signals with coordinate-aware encoders for global structure, and (iii) adopts an axial-global attention decoder to capture OD-specific competitive dependencies. For OD flow generation, GeoFlow is paired with flow matching models to produce more authentic and diverse mobility samples. Empirically, GeoFlow achieves superior performance in predictive accuracy, while substantially improving generative fidelity and diversity. Ablation and analytical studies confirm the contribution of each component. Code is available at [https://github.com/ZheruiHuang/GeoFlow](https://github.com/ZheruiHuang/GeoFlow).

Current video diffusion models generate visually compelling content but often struggle with physical motion, producing subtle artifacts like rubber-sheet deformations and inconsistent object motion. We introduce a frequency-domain physics prior that improves motion plausibility without modifying model architectures. Our method decomposes common motion patterns (translation, rotation, scaling) into lightweight spectral losses. Applied to Open-Sora, MVDIT, and Hunyuan, our approach improves both motion accuracy and action recognition by ∼11\% on average on OpenVID-1M (relative), while maintaining visual quality. Additional results on Wan 2.1-14B show consistent gains on video-quality and physics-oriented metrics. User studies show 74-83\% preference for our physics-enhanced videos. It also reduces warping error by 22-37\% (depending on the backbone) and improves temporal consistency scores. These results indicate that simple, global spectral cues are an effective drop-in regularizer for physically plausible motion in video diffusion.

Adversarial purification uses generative models to restore clean data distributions from unseen attacks without retraining classifiers. However, unimodal diffusion-based approaches struggle to preserve semantic consistency, while recent multimodal variants rely on computationally expensive adversarial training or distillation. Both approaches often lack theoretical guarantees. In this work, we propose MultiDAP, a novel framework leveraging multimodal diffusion models for efficient adversarial purification. MultiDAP first learns continuous class-agnostic prompts from clean data to capture rich semantic priors, replacing rigid hand-crafted templates. Guided by these prompts, MultiDAP purifies adversarial inputs by minimizing a regularized DDPM loss for only a few steps (e.g., 5-20). We provide theoretical guarantees for both the likelihood improvement via prompt learning and the convergence of the purification process. Extensive experiments on CIFAR-10, CIFAR-100, and ImageNet-1K demonstrate that MultiDAP matches the robustness of state-of-the-art baselines but with improved efficiency.

Learning on graphs with missing node attributes is a prevalent yet challenging problem in real-world scenarios, as graph neural networks (GNNs) typically rely on complete attribute information. Existing solutions often employ adversarial learning in a shared latent space to align graph structure and attributes. However, these methods frequently suffer from training instability and mode collapse, failing to fully capture the complex, multi-modal joint distribution of topology and features. To address these limitations, we present GLAD, a novel generative framework for robust node attribute completion. GLAD leverages the strong generative capabilities of diffusion models to learn the conditional distribution of attributes given the graph structure within a decoupled latent space. Unlike previous unidirectional approaches, GLAD introduces a robust bidirectional alignment mechanism. Specifically, we incorporate a structure reconstruction constraint during training and structure-aware classifier-free guidance during sampling, ensuring that generated attributes are not only plausible but also maintain strict topological consistency with the underlying graph. Theoretically, we show that GLAD maximizes a tighter variational lower bound on the joint log-likelihood compared to GAN-based predecessors, leading to superior mode coverage. Extensive experiments on large-scale benchmarks demonstrate that GLAD significantly outperforms state-of-the-art baselines in both attribute recovery quality and downstream task performance.

Riemannian diffusion models generalize score-based generative modeling to manifold-supported data via stochastic diffusion equations on the manifold. However, training requires sampling from and differentiating the manifold heat kernel, which is rarely available in closed form beyond a few highly symmetric manifolds. We propose a general approach that approximates the heat kernel by directly solving the manifold heat equation with a physics-informed neural network (PINN). Given an explicit manifold specification, we choose a coordinate system, derive the corresponding heat (Fokker--Planck) equation and a short-time asymptotic approximation, and then train a PINN to learn the log heat kernel. The resulting surrogate enables both forward noising (heat-kernel sampling) and conditional-score evaluation for denoising score matching. We demonstrate the method on diverse manifolds including $S^2$, $SO(3)$, $\mathrm{SPD}(n)$, and permutation-quotiented point clouds.

Low-rank tensor decomposition (TD) is usually effective on clean, fully observed data, but it often degrades under severe missingness or noise. Low-rankness is itself a useful but limited structural prior, and additional handcrafted priors (e.g., sparsity or smoothness) still fall short of capturing the rich statistics of real-world data. To compensate for this weak inductive bias under heavy corruption, one would like to inject a learned, data-driven prior; however, the state-of-the-art diffusion models are not readily compatible with current TD and tractable posterior inference. To address these challenges, we introduce DiffBCP, a hybrid-prior Bayesian CP decomposition framework that couples a cumulative shrinkage process prior over the CP factors for automatic rank selection with an off-the-shelf pre-trained diffusion model as an implicit data prior on the reconstructed tensor. To make posterior inference tractable despite the coupling among the likelihood, low-rank constraint, and diffusion prior, we develop a split Gibbs sampler: CP factors admit conjugate updates, while the diffusion block is sampled via low-rank-guided denoising. A noise-adaptive coupling schedule further reduces sensitivity to hand-tuned annealing. Experiments on image inpainting and denoising, including high-resolution out-of-distribution images, show consistent gains over Bayesian, nonlinear, and plug-and-play TD baselines.

Backpropagation (BP) remains the dominant training paradigm for deep neural networks, yet its reliance on global gradient propagation fundamentally induces update locking problem, enforcing strong inter-layer dependencies in parameter updates. To address this limitation, we propose Depth-progressive Monotonic Learning (DMoL), a training scheme that assigns layer-wise local belief objectives and incrementally refines them across network depth, enabling unlocked parameter updates. As a result, DMoL supports dynamic modification of network depth during training, adapting to available compute and device resources while maintaining stable optimization. We provide theoretical guarantees that layer-wise local belief objectives improve monotonically with increasing depth and converge exponentially. Empirically, DMoL consistently matches or outperforms BP across diverse tasks, yielding a 4.3\% accuracy gain on CIFAR-100, mitigating over-smoothing in deep graph neural networks (+37.5\% on Cora), and reducing the final loss by over 35\% in diffusion model training, highlighting its robustness and flexibility as an alternative to BP. The code is publicly available at: https://github.com/ychAlbert/DMoL.

New technologies such as Rectified Flow and Flow Matching have significantly improved the performance of generative models in the past two years, especially in terms of control accuracy, generation quality, and generation efficiency. However, due to some differences in its theory, design, and existing diffusion models, the existing acceleration methods cannot be directly applied to the Rectified Flow model. In this article, we have comprehensively implemented an overall acceleration pipeline from the aspects of theory, design, and reasoning strategies. This pipeline uses new methods such as batch processing with a new velocity field, vectorization of heterogeneous time-step batch processing, and dynamic TensorRT compilation for the new methods to comprehensively accelerate related models based on flow models. Currently, the existing public methods usually achieve an acceleration of 18%, while experiments have proved that our new method can accelerate the 512$\times$512 image generation speed to up to 611%, which is far beyond the current non-generalized acceleration methods. Project page at [https://world-snapshot.github.io/StreamFlow/](https://world-snapshot.github.io/StreamFlow/).

This paper approaches the fundamental challenge of accelerating the inherently autoregressive nature of gradient descent (GD) like SGD and Adam through a dynamic system perspective. Specifically, we introduce a unified framework that recasts the autoregressive GD process as solving a system of triangular nonlinear equations (TNEs), thereby enabling \textit{step-parallel} training, where gradients for different GD steps are computed concurrently without sequential dependencies. Within this generic framework, we establish that: (1) the TNE system admits a unique solution corresponding precisely to the autoregressive GD iterative trajectory; (2) solving the TNEs system guarantees convergence to the GD iterative trajectory in at most the equal iterations. Building on these insights, we present \textit{PASO}, the first step-parallel optimizer for accelerating a broad class of GD-based optimizers like SGD and Adam. Extensive experiments (\textit{e.g.}, Llama-3.2-1B and diffusion model) validate that PASO achieves up to \textbf{21}$\times$ reduction in GD steps and \textbf{4.5}$\times$ speedup in wall-clock time, with no model quality loss. Source code is available at: \url{https://github.com/Jianrong-Lu/PASO.git}.

In discrete generative modeling, two dominant paradigms demonstrate divergent capabilities: Masked Diffusion Language Models (MDLM) excel at semantic understanding and zero-shot generalization, whereas Uniform-noise Diffusion Language Models (UDLM) achieve strong few-step generation quality, yet neither attains balanced performance across both dimensions. To address this, we propose XDLM, which bridges the two paradigms via a stationary noise kernel. XDLM offers two key contributions: it provides (1) a principled theoretical unification of MDLM and UDLM, recovering each paradigm as a special case; and (2) an alleviated memory bottleneck enabled by an algebraic simplification of the posterior probabilities. Experiments demonstrate that XDLM advances the Pareto frontier between understanding capability and generation quality. Quantitatively, XDLM surpasses UDLM by 5.4 points on zero-shot text benchmarks and outperforms MDLM in few-step image generation (FID 54.1 vs. 80.8). When scaled to tune an 8B-parameter large language model, XDLM achieves 15.0 MBPP in just 32 steps, effectively doubling the baseline performance. Finally, analysis of training dynamics reveals XDLM’s superior potential for long-term scaling. Code is available at [https://github.com/MzeroMiko/XDLM](https://github.com/MzeroMiko/XDLM).

Diffusion language models (dLLMs) recently emerged as a promising alternative to auto-regressive LLMs. The latest works further extended it to multimodal understanding and generation tasks. In this work, we propose LaViDa-R1, a multimodal, general-purpose reasoning dLLM. Unlike existing works that build reasoning dLLMs through task-specific reinforcement learning, LaViDa-R1 incorporates diverse multimodal understanding and generation tasks in a unified manner. In particular, LaViDa-R1 is built with a novel unified post-training framework that seamlessly integrates supervised finetuning (SFT) and multi-task reinforcement learning (RL). It employs several novel training techniques, including answer-forcing, tree search, and complementary likelihood estimation, to enhance effectiveness and scalability. Extensive experiments demonstrate LaViDa-R1's strong performance on a wide range of multimodal tasks, including visual math reasoning, reason-intensive grounding, and image editing.

Recent years have witnessed significant progress in developing effective diffusion models. Parallel sampling is a promising recent approach that reformulates the sequential denoising process as solving a system of nonlinear equations, and it can be combined with other acceleration techniques. However, current progress is limited by the trade-off between high fidelity and computational efficiency. This paper addresses the challenge of scaling to high-dimensional, multi-modal generation. Specifically, we present ROPA (Robust Parallel Diffusion Sampling), which takes into account the properties of the denoising process and solves the linear system using adaptive local sparsity to achieve stable parallel sampling. Extensive experiments demonstrate ROPA’s effectiveness: it significantly accelerates sampling across diverse image and video diffusion models, achieving up to $2.9\times$ speedup with eight core, an improvement of 20.8\% over baselines without sacrificing sample quality. ROPA enables parallel sampling methods to provide a solid foundation for real-time, high-fidelity diffusion generation.

We investigate the role of network architecture in shaping the inductive biases of modern score-based generative models. To this end, we introduce the Score Anisotropy Directions (SADs), architecture-dependent directions that reveal how different networks preferentially capture data structure. Our analysis suggests that SADs form adaptive bases aligned with the architecture's output geometry, providing a principled way to predict generalization ability in score models prior to training. Through both synthetic data and standard image benchmarks, we demonstrate that SADs reliably capture fine-grained model behavior and correlate with downstream performance, as measured by Wasserstein metrics. Our work offers a new lens for explaining and predicting directional biases of generative models.

Diffusion-based language models (dLLMs) enable parallel token generation through iterative denoising, but existing decoding strategies collapse to single-token generation under low confidence, severely limiting throughput. Unlike autoregressive models where speculative decoding operates on token sequences in a fixed left-to-right order, dLLMs require speculating over \emph{denoising trajectories}—sequences of multi-token updates with explicit positions and unmasking orders. We develop a trajectory-level speculative framework that constructs draft denoising trajectories via confidence-stratified tree exploration and verifies them through blockwise parallel evaluation with bidirectional attention masking. Our method further introduces inter-block speculation, exploiting diffusion models' bidirectional structure to perform cross-block lookahead. We formally characterize when this approach is exact and identify trajectory drift as the fundamental cost of increased parallelism. Building on Fast-dLLM's dual-cache infrastructure, our framework reduces denoising iterations by 30-40\% and increases tokens-per-step from 2.6 to 4.3, achieving 7-14$\times$ speedup over vanilla dLLMs and 1.3$\times$ over Fast-dLLM with less than 1\% accuracy change across reasoning and code benchmarks.

Symbolic regression (SR) aims to discover interpretable mathematical expressions from observed data. While recent generative approaches have shown promise in treating SR as machine translation or multimodal learning tasks using NN methods, they suffer from uncontrollable generation process and training-evaluation misalignment. The training objectives (average cross-entropy loss on a token level across the distribution of historical data) differ from the evaluation metric (fitting error for every test data / complexity), necessitating extensive heuristic post-processing. On the other hand, direct optimization methods suffer from an exponential slowdown as the dimensionality increases, non-differentiability and local optima traps. We propose **MOD-SR**, unifying multimodal distribution learning during training with direct optimization at inference time. This is achieved by modeling the task as $p(x_0 \mid \mathcal{D}, y^*)$ and employing gradient-guided diffusion in embedding space, enhanced by contrastive learning and representation alignment. Furthermore, we introduce DFEX, a fixed-depth tree relaxation method that ensures differentiability for effective gradient guidance during inference. Experiments demonstrate that MOD-SR achieves superior performance on diverse benchmarks through a unified framework integrating distribution learning and optimization. Our code is available at [https://github.com/KROX777/MOD-SR](https://github.com/KROX777/MOD-SR).

Real-world super-resolution (SR) at large upscaling factors (i.e., ≥ 4×) remains difficult due to complex real-image degradations. HYPIR, a leading diffusion-based restoration model, performs strongly on many inputs, yet for a non-trivial portion of more challenging cases a single forward step does not fully recover fine-grained details. A naive two-stage cascade improves visual quality, but introduces over-saturation, weak texture details, and high inference latency. To address these issues, this paper proposes HYPIR++. It removes the degradation removal encoder and noise augmentation modules to better preserve fidelity cues from low-quality inputs. Equipped with an optimized latent ConvNeXt and a latent patch discriminator, HYPIR++ supports latentspace adversarial learning for clearer details and more stable local structures. It further shortens text sequences and replaces full attention with sparse neighbor attention, enabling efficient highresolution inference without tiling. Experiments show that HYPIR++ improves perceptual quality and runs 1.71× faster than HYPIR on large-factor real-world SR

Discrete Diffusion Large Language Models (dLLMs) have recently emerged as a promising non-autoregressive paradigm, offering faster inference while achieving strong performance in code generation and mathematical reasoning tasks. In this work, we show that dLLMs’ decoding mechanism not only improves utility but also enables effective model attribution: by analyzing a response’s decoding trajectory, we can identify its source model and help mitigate risks from model misuse. A key challenge is the diversity of attribution scenarios, ranging from distinguishing different models to identifying different checkpoints or backups of the same model. To ensure broad applicability, we focus on two core questions: what information to extract from the decoding trajectory, and how to use it effectively. We first observe that per-step model confidence is ineffective, as the bidirectional nature of dLLMs causes mutual influence among decoded tokens, leading to highly redundant confidence signals that obscure structural information about decoding order and dependencies. To overcome this, we propose a novel information extraction scheme called the \textit{Directed Decoding Map (DDM)}, which captures structural relationships between decoding steps and reveals model-specific behaviors. Furthermore, to fully leverage the extracted structure, we propose \textit{Gaussian-Trajectory Attribution (GTA)}, which fits a cell-wise Gaussian distribution at each decoding position for each model and uses log-likelihood differences between trajectories as the attribution score. Extensive experiments across diverse models, datasets and different model access assumptions validate the effectiveness of our approach.

Conditional flow matching has emerged as a powerful generative modeling framework that learns a vector field to transport an initial distribution toward a target data distribution. However, theoretical understanding of its out-of-distribution (OOD) performance under unseen conditions remains limited. In this work, we establish a rigorous geometric formulation to decompose the source of generalization error. We treat the conditional task as a map from the condition space to the Wasserstein space and derive a generalization bound under a coarse embedding assumption. The resulting decomposition separates OOD error into three tractable components: *Interpolation Sparsity*, *Geometric Distortion*, and *In-Distribution Fit*. Our empirical evaluation confirms that this framework demonstrates three key functions: (1) it acts as a diagnostic tool that tracks the dynamics of generalization during training; (2) it identifies dataset-specific failure modes (e.g., topological gaps, geometric instability); and (3) it enables mathematically motivated interventions that yield predictable gains by minimizing specific terms.

Transformers have revolutionized deep learning across various domains but understanding the precise token dynamics remains a theoretical challenge. Existing theories of deep Transformers with layer normalization typically predict that tokens cluster to a single point; however, these results rely on deterministic weight assumptions, which fail to capture the standard initialization scheme in Transformers. In this work, we show that accounting for the intrinsic stochasticity of random initialization alters this picture. More precisely, we analyze deep Transformers where noise arises from the random initialization of value matrices. Under diffusion scaling and token-wise RMS normalization, we prove that, as the number of Transformer layers goes to infinity, the discrete token dynamics converge to an interacting-particle system on the sphere where tokens are driven by a *common* matrix-valued Brownian noise. In this limit, we show that initialization noise prevents the collapse to a single cluster predicted by deterministic models. For two tokens, we prove a phase transition governed by the interaction strength and the token dimension: unlike deterministic attention flows, antipodal configurations become attracting with positive probability. Numerical experiments confirm the predicted transition, reveal that antipodal formations persist for more than two tokens, and demonstrate that suppressing the intrinsic noise degrades accuracy.