Related papers: Rectified Flows for Fast Multiscale Fluid Flow Mod…

We present a concise, self-contained derivation of diffusion-based generative models. Starting from basic properties of Gaussian distributions (densities, quadratic expectations, re-parameterisation, products, and KL divergences), we…

Diffusion models have significantly improved the quality and diversity of audio generation but are hindered by slow inference speed. Rectified flow enhances inference speed by learning straight-line ordinary differential equation (ODE)…

Generating high-quality time-series data is challenging because real-world signals often exhibit multimodal patterns and multiscale dynamics, including oscillations and high-frequency variations. Flow Matching (FM) offers an efficient…

This study proposes a new discrete neural operator for surrogate modeling of transient Darcy flow fields in heterogeneous porous media with random parameters. The new method integrates temporal encoding, operator learning and UNet to…

Bayesian inverse modeling is important for a better understanding of hydrological processes. However, this approach can be computationally demanding, as it usually requires a large number of model evaluations. To address this issue, one can…

Diffusion-based generative processes, formulated as differential equation solving, frequently balance computational speed with sample quality. Our theoretical investigation of ODE- and SDE-based solvers reveals complementary weaknesses: ODE…

We introduce and test methods for the calibration of the diffusion term in Stochastic Partial Differential Equations (SPDEs) describing fluids. We take two approaches, one uses ideas from the singular value decomposition and the Biot-Savart…

A recent study in turbulent flow simulation demonstrated the potential of generative diffusion models for fast 3D surrogate modeling. This approach eliminates the need for specifying initial states or performing lengthy simulations,…

The Bayesian uncertainty quantification technique has become well established in turbulence modeling over the past few years. However, it is computationally expensive to construct a globally accurate surrogate model for Bayesian inference…

Analyzing unsteady fluid flows often requires access to the full distribution of possible temporal states, yet conventional PDE solvers are computationally prohibitive and learned time-stepping surrogates quickly accumulate error over long…

This work proposes a statistically enhanced framework to address the instability and limited predictive capability of conventional Galerkin-Proper Orthogonal Decomposition (Galerkin-POD) models. The method reformulates the correction of the…

Diffusion models (DMs) have demonstrated remarkable success in real-world image super-resolution (SR), yet their reliance on time-consuming multi-step sampling largely hinders their practical applications. While recent efforts have…

We present theoretical convergence guarantees for ODE-based generative models, specifically flow matching. We use a pre-trained autoencoder network to map high-dimensional original inputs to a low-dimensional latent space, where a…

Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…

The performance of flow matching and diffusion models can be greatly improved at inference time using reward alignment algorithms, yet efficiency remains a major limitation. While several algorithms were proposed, we demonstrate that a…

Accurate channel impulse response (CIR) modeling in molecular communication (MC) often requires solving coupled reactive diffusion-advection equations, which is computationally expensive for large parameter sweeps or design loops. We…

High-fidelity, high-resolution numerical simulations are crucial for studying complex multiscale phenomena in fluid dynamics, such as turbulent flows and ocean waves. However, direct numerical simulations with high-resolution solvers are…

This paper presents a novel methodology for tractably solving optimal control and offline reinforcement learning problems for high-dimensional systems. This work is motivated by the ongoing challenges of safety, computation, and optimality…

We present a discretization-free scalable framework for solving a large class of mass-conserving partial differential equations (PDEs), including the time-dependent Fokker-Planck equation and the Wasserstein gradient flow. The main…

Flow matching has recently emerged as a principled framework for learning continuous-time transport maps, enabling efficient ODE-based sampling without relying on stochastic diffusion processes. While generative modeling has shown promise…