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Diffusion Transformers with Representation Autoencoders
Boyang Zheng, Nanye Ma, Shengbang Tong, Saining Xie
https://arxiv.org/abs/2510.11690 https://arxiv.…

Diffusion Transformers with Representation Autoencoders
Latent generative modeling, where a pretrained autoencoder maps pixels into a latent space for the diffusion process, has become the standard strategy for Diffusion Transformers (DiT); however, the autoencoder component has barely evolved. Most DiTs continue to rely on the original VAE encoder, which introduces several limitations: outdated backbones that compromise architectural simplicity, low-dimensional latent spaces that restrict information capacity, and weak representations that result f…

SPG: Sandwiched Policy Gradient for Masked Diffusion Language Models
Chengyu Wang, Paria Rashidinejad, DiJia Su, Song Jiang, Sid Wang, Siyan Zhao, Cai Zhou, Shannon Zejiang Shen, Feiyu Chen, Tommi Jaakkola, Yuandong Tian, Bo Liu
https://arxiv.org/abs/2510.09541

SPG: Sandwiched Policy Gradient for Masked Diffusion Language Models
Diffusion large language models (dLLMs) are emerging as an efficient alternative to autoregressive models due to their ability to decode multiple tokens in parallel. However, aligning dLLMs with human preferences or task-specific rewards via reinforcement learning (RL) is challenging because their intractable log-likelihood precludes the direct application of standard policy gradient methods. While prior work uses surrogates like the evidence lower bound (ELBO), these one-sided approximations c…

Multiscale Graph Reduction for Heterogeneous and Anisotropic Discrete Diffusion Processes
Maria Vasilyeva, James Brannick, Ben S. Southworth
https://arxiv.org/abs/2510.10894 htt…

Multiscale Graph Reduction for Heterogeneous and Anisotropic Discrete Diffusion Processes
We present multiscale graph-based reduction algorithms for upscaling heterogeneous and anisotropic diffusion problems. The proposed coarsening approaches begin by constructing a partitioning of the computational domain into a set of balanced local subdomains, resulting in a standard type of domain decomposition. Given this initial decomposition, general coarsening techniques based on spectral clustering are applied within each subgraph in order to accurately identify the key microscopic feature…

Large Scale Diffusion Distillation via Score-Regularized Continuous-Time Consistency
Kaiwen Zheng, Yuji Wang, Qianli Ma, Huayu Chen, Jintao Zhang, Yogesh Balaji, Jianfei Chen, Ming-Yu Liu, Jun Zhu, Qinsheng Zhang
https://arxiv.org/abs/2510.08431

Large Scale Diffusion Distillation via Score-Regularized Continuous-Time Consistency
This work represents the first effort to scale up continuous-time consistency distillation to general application-level image and video diffusion models. Although continuous-time consistency model (sCM) is theoretically principled and empirically powerful for accelerating academic-scale diffusion, its applicability to large-scale text-to-image and video tasks remains unclear due to infrastructure challenges in Jacobian-vector product (JVP) computation and the limitations of standard evaluation …

Continuously Augmented Discrete Diffusion model for Categorical Generative Modeling
Huangjie Zheng, Shansan Gong, Ruixiang Zhang, Tianrong Chen, Jiatao Gu, Mingyuan Zhou, Navdeep Jaitly, Yizhe Zhang
https://arxiv.org/abs/2510.01329

Continuously Augmented Discrete Diffusion model for Categorical Generative Modeling
Standard discrete diffusion models treat all unobserved states identically by mapping them to an absorbing [MASK] token. This creates an 'information void' where semantic information that could be inferred from unmasked tokens is lost between denoising steps. We introduce Continuously Augmented Discrete Diffusion (CADD), a framework that augments the discrete state space with a paired diffusion in a continuous latent space. This yields graded, gradually corrupted states in which masked tokens a…

Steady-State Spread Bounds for Graph Diffusion via Laplacian Regularisation
Ardavan Rahimian
https://arxiv.org/abs/2510.04924 https://arxiv.org/pdf/2510.04…

Steady-State Spread Bounds for Graph Diffusion via Laplacian Regularisation
We study how far a diffusion process on a graph can drift from a designed starting pattern when that pattern is produced using Laplacian regularisation. Under standard stability conditions for undirected, entrywise nonnegative graphs, we give a closed-form, instance-specific upper bound on the steady-state spread, measured as the relative change between the final and initial profiles. The bound separates two effects: (i) an irreducible term determined by the graph's maximum node degree, and (ii…

Turing instability and 2-D pattern formation in reaction-diffusion systems derived from kinetic theory
Stefano Boccelli, Giorgio Martal\`o, Romina Travaglini
https://arxiv.org/abs/2509.20268

Turing instability and 2-D pattern formation in reaction-diffusion systems derived from kinetic theory
We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of Brusselator type, which, compared with the classical formulation, presents an additional parameter whose role in stability and pattern formation is discussed. In the second framework, the system exhibits standard nonlinear diffusion terms typical of predator-pr…

Self-Speculative Masked Diffusions
Andrew Campbell, Valentin De Bortoli, Jiaxin Shi, Arnaud Doucet
https://arxiv.org/abs/2510.03929 https://arxiv.org/pdf/2…

Self-Speculative Masked Diffusions
We present self-speculative masked diffusions, a new class of masked diffusion generative models for discrete data that require significantly fewer function evaluations to generate samples. Standard masked diffusion models predict factorized logits over currently masked positions. A number of masked positions are then sampled, however, the factorization approximation means that sampling too many positions in one go leads to poor sample quality. As a result, many simulation steps and therefore n…

Do You Know Where Your Camera Is? View-Invariant Policy Learning with Camera Conditioning
Tianchong Jiang, Jingtian Ji, Xiangshan Tan, Jiading Fang, Anand Bhattad, Vitor Guizilini, Matthew R. Walter
https://arxiv.org/abs/2510.02268

Do You Know Where Your Camera Is? View-Invariant Policy Learning with Camera Conditioning
We study view-invariant imitation learning by explicitly conditioning policies on camera extrinsics. Using Plucker embeddings of per-pixel rays, we show that conditioning on extrinsics significantly improves generalization across viewpoints for standard behavior cloning policies, including ACT, Diffusion Policy, and SmolVLA. To evaluate policy robustness under realistic viewpoint shifts, we introduce six manipulation tasks in RoboSuite and ManiSkill that pair "fixed" and "randomized" scene vari…

Stationarity preserving nodal Finite Element methods for multi-dimensional linear hyperbolic balance laws via a Global Flux quadrature formulation
Wasilij Barsukow, Mario Ricchiuto, Davide Torlo
https://arxiv.org/abs/2510.02928

Stationarity preserving nodal Finite Element methods for multi-dimensional linear hyperbolic balance laws via a Global Flux quadrature formulation
We consider linear, hyperbolic systems of balance laws in several space dimensions. They possess non-trivial steady states, which result from the equilibrium between derivatives of the unknowns in different directions, and the sources. Standard numerical methods fail to account for this equilibrium, and include stabilization that destroys it. This manifests itself in a diffusion of states that are sup- posed to remain stationary. We derive new stabilized high-order Finite Element methods based …

Neural Jump ODEs as Generative Models
Robert A. Crowell, Florian Krach, Josef Teichmann
https://arxiv.org/abs/2510.02757 https://arxiv.org/pdf/2510.02757…

Neural Jump ODEs as Generative Models
In this work, we explore how Neural Jump ODEs (NJODEs) can be used as generative models for Itô processes. Given (discrete observations of) samples of a fixed underlying Itô process, the NJODE framework can be used to approximate the drift and diffusion coefficients of the process. Under standard regularity assumptions on the Itô processes, we prove that, in the limit, we recover the true parameters with our approximation. Hence, using these learned coefficients to sample from the correspond…

MIMIC-D: Multi-modal Imitation for MultI-agent Coordination with Decentralized Diffusion Policies
Dayi Dong, Maulik Bhatt, Seoyeon Choi, Negar Mehr
https://arxiv.org/abs/2509.14159

MIMIC-D: Multi-modal Imitation for MultI-agent Coordination with Decentralized Diffusion Policies
As robots become more integrated in society, their ability to coordinate with other robots and humans on multi-modal tasks (those with multiple valid solutions) is crucial. We propose to learn such behaviors from expert demonstrations via imitation learning (IL). However, when expert demonstrations are multi-modal, standard IL approaches can struggle to capture the diverse strategies, hindering effective coordination. Diffusion models are known to be effective at handling complex multi-modal tr…

A Statistical Benchmark for Diffusion Posterior Sampling Algorithms
Martin Zach, Youssef Haouchat, Michael Unser
https://arxiv.org/abs/2509.12821 https://a…

A Statistical Benchmark for Diffusion Posterior Sampling Algorithms
We propose a statistical benchmark for diffusion posterior sampling (DPS) algorithms for Bayesian linear inverse problems. The benchmark synthesizes signals from sparse Lévy-process priors whose posteriors admit efficient Gibbs methods. These Gibbs methods can be used to obtain gold-standard posterior samples that can be compared to the samples obtained by the DPS algorithms. By using the Gibbs methods for the resolution of the denoising problems in the reverse diffusion, the framework also is…

Solving time-fractional diffusion equations with Robin boundary conditions via fractional Hamiltonian boundary value methods
Qian Luo, Aiguo Xiao, Xiaoqiang Yan, Jingmin Xia
https://arxiv.org/abs/2509.17793

Solving time-fractional diffusion equations with Robin boundary conditions via fractional Hamiltonian boundary value methods
In this paper, we propose a novel numerical scheme for solving time-fractional reaction-diffusion problems with Robin boundary conditions, where the time derivative is in the Caputo sense of order $α\in(0,1)$. The existence and uniqueness of the solution is proved. Our proposed method is based on the spectral collocation method in space and Fractional Hamiltonian boundary value methods in time. For the considered spectral collocation method, the basis functions used are not the standard polyno…

Anchored Langevin Algorithms
Mert Gurbuzbalaban, Hoang M. Nguyen, Xicheng Zhang, Lingjiong Zhu
https://arxiv.org/abs/2509.19455 https://arxiv.org/pdf/2509.…

Anchored Langevin Algorithms
Standard first-order Langevin algorithms such as the unadjusted Langevin algorithm (ULA) are obtained by discretizing the Langevin diffusion and are widely used for sampling in machine learning because they scale to high dimensions and large datasets. However, they face two key limitations: (i) they require differentiable log-densities, excluding targets with non-differentiable components; and (ii) they generally fail to sample heavy-tailed targets. We propose anchored Langevin dynamics, a unif…

Adaptive least-squares space-time finite element methods for convection-diffusion problems
Christian K\"othe, Olaf Steinbach
https://arxiv.org/abs/2509.11955 https://

Adaptive least-squares space-time finite element methods for convection-diffusion problems
In this paper we formulate and analyse adaptive (space-time) least-squares finite element methods for the solution of convection-diffusion equations. The convective derivative $\mathbf{v} \cdot \nabla u$ is considered as part of the total time derivative $\frac{d}{dt}u = \partial_t u + \mathbf{v} \cdot \nabla u$, and therefore we can use a rather standard stability and error analysis for related space-time finite element methods. For stationary problems we restrict the ansatz space $H^1_0(Ω)$ …

CollabVLA: Self-Reflective Vision-Language-Action Model Dreaming Together with Human
Nan Sun, Yongchang Li, Chenxu Wang, Huiying Li, Huaping Liu
https://arxiv.org/abs/2509.14889

CollabVLA: Self-Reflective Vision-Language-Action Model Dreaming Together with Human
In this work, we present CollabVLA, a self-reflective vision-language-action framework that transforms a standard visuomotor policy into a collaborative assistant. CollabVLA tackles key limitations of prior VLAs, including domain overfitting, non-interpretable reasoning, and the high latency of auxiliary generative models, by integrating VLM-based reflective reasoning with diffusion-based action generation under a mixture-of-experts design. Through a two-stage training recipe of action groundin…

Radiolunadiff: Estimation of wireless network signal strength in lunar terrain
Paolo Torrado, Anders Pearson, Jason Klein, Alexander Moscibroda, Joshua Smith
https://arxiv.org/abs/2509.14559

Radiolunadiff: Estimation of wireless network signal strength in lunar terrain
In this paper, we propose a novel physics-informed deep learning architecture for predicting radio maps over lunar terrain. Our approach integrates a physics-based lunar terrain generator, which produces realistic topography informed by publicly available NASA data, with a ray-tracing engine to create a high-fidelity dataset of radio propagation scenarios. Building on this dataset, we introduce a triplet-UNet architecture, consisting of two standard UNets and a diffusion network, to model compl…

Adapting Noise to Data: Generative Flows from 1D Processes
Jannis Chemseddine, Gregor Kornhardt, Richard Duong, Gabriele Steidl
https://arxiv.org/abs/2510.12636 https://

Adapting Noise to Data: Generative Flows from 1D Processes
We introduce a general framework for constructing generative models using one-dimensional noising processes. Beyond diffusion processes, we outline examples that demonstrate the flexibility of our approach. Motivated by this, we propose a novel framework in which the 1D processes themselves are learnable, achieved by parameterizing the noise distribution through quantile functions that adapt to the data. Our construction integrates seamlessly with standard objectives, including Flow Matching an…

Error analysis of a fully discrete structure-preserving finite element scheme for a diffuse-interface model of tumour growth
Agus L. Soenjaya, Ping Lin, Thanh Tran
https://arxiv.org/abs/2509.14486

Error analysis of a fully discrete structure-preserving finite element scheme for a diffuse-interface model of tumour growth
We develop a fully discrete structure-preserving finite element method for a diffuse-interface model of tumour growth. The system couples a Cahn--Hilliard type equation with a nonlinear reaction-diffusion equation for nutrient concentration and admits a dissipative energy law at the continuous level. For the discretisation, we employ a scalar auxiliary variable (SAV) formulation together with a mixed finite element method for the Cahn--Hilliard part and standard conforming finite elements for t…