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We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiation-hydrodynamic code with adaptive mesh refinement (AMR). The…
We study the long-time behavior of a particle in $\mathbb{R}^d$, $d \geq 2$, subject to molecular diffusion and advection by a random incompressible flow. The velocity field is the divergence of a stationary random stream matrix $\mathbf{k}…
Diffusion and flow models have become the dominant paradigm for generative modeling on Riemannian manifolds, with successful applications in protein backbone generation and DNA sequence design. However, these methods require tens to…
Diffusion models have seen widespread adoption for text-driven human motion generation and related tasks due to their impressive generative capabilities and flexibility. However, current motion diffusion models face two major limitations: a…
Modern generative modeling is dominated by transport from a noise prior to data. We propose an alternative paradigm in which generation is performed by a discrete stochastic dynamics that leaves the data distribution invariant, initialized…
Transient growth analysis has been extensively studied in asymptotically stable flows to identify their short-term amplification of perturbations. Generally, in global transient growth analyses, matrix-free methods are adopted, requiring…
Score-based Generative Models (SGMs) have demonstrated exceptional synthesis outcomes across various tasks. However, the current design landscape of the forward diffusion process remains largely untapped and often relies on physical…
We introduce the Flow Stochastic Segmentation Network (Flow-SSN), a generative segmentation model family featuring discrete-time autoregressive and modern continuous-time flow variants. We prove fundamental limitations of the low-rank…
In this work, we seek to simulate rare transitions between metastable states using score-based generative models. An efficient method for generating high-quality transition paths is valuable for the study of molecular systems since data is…
Generative models have achieved remarkable progress with the emergence of flow matching (FM). It has demonstrated strong generative capabilities and attracted significant attention as a simulation-free flow-based framework capable of…
We suggest a new multi-modal algorithm for joint inference of paired structurally aligned samples with Rectified Flow models. While some existing methods propose a codependent generation process, they do not view the problem of joint…
We propose a novel data-driven method to accelerate the convergence of Alternating Direction Method of Multipliers (ADMM) for solving distributed DC optimal power flow (DC-OPF) where lines are shared between independent network partitions.…
We propose a unified, few-step generative modeling framework based on \emph{cumulative flow maps} for long-range transport in probability space, inspired by flow-map techniques for physical transport and dynamics. At its core is a…
Flow-based generative models have recently shown impressive performance for conditional generation tasks, such as text-to-image generation. However, current methods transform a general unimodal noise distribution to a specific mode of the…
High-order Graph Neural Networks (HO-GNNs) have been developed to infer consistent latent spaces in the heterophilic regime, where the label distribution is not correlated with the graph structure. However, most of the existing HO-GNNs are…
Diffusion models deliver state-of-the-art generative performance across diverse modalities but remain computationally expensive due to their inherently iterative sampling process. Existing training-free acceleration methods typically…
Channel estimation is a fundamental challenge in massive multiple-input multiple-output systems, where estimation accuracy governs the spectral efficiency and link reliability. In this work, we introduce Recursive Flow (RC-Flow), a novel…
Existing graph generative models often face a critical trade-off between sample quality and generation speed. We introduce Autoregressive Noisy Filtration Modeling (ANFM), a flexible autoregressive framework that addresses both challenges.…
High-dimensional generative modeling is fundamentally a manifold-learning problem: real data concentrate near a low-dimensional structure embedded in the ambient space. Effective generators must therefore balance support fidelity -- placing…
Generating long-term, coherent, and realistic music-conditioned dance sequences remains a challenging task in human motion synthesis. Existing approaches exhibit critical limitations: motion graph methods rely on fixed template libraries,…