Related papers: FlowDPS: Flow-Driven Posterior Sampling for Invers…

Inverse problems, which involve estimating parameters from incomplete or noisy observations, arise in various fields such as medical imaging, geophysics, and signal processing. These problems are often ill-posed, requiring regularization…

Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…

Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate…

Diffusion Inverse Solvers (DIS) are designed to sample from the conditional distribution $p_{\theta}(X_0|y)$, with a predefined diffusion model $p_{\theta}(X_0)$, an operator $f(\cdot)$, and a measurement $y=f(x'_0)$ derived from an unknown…

Diffusion probabilistic models (DPMs) are a key component in modern generative models. DPM-solvers have achieved reduced latency and enhanced quality significantly, but have posed challenges to find the exact inverse (i.e., finding the…

Diffusion models have been firmly established as principled zero-shot solvers for linear and nonlinear inverse problems, owing to their powerful image prior and iterative sampling algorithm. These approaches often rely on Tweedie's formula,…

Generative models, particularly diffusion model, have emerged as powerful tools for sequential recommendation. However, accurately modeling user preferences remains challenging due to the noise perturbations inherent in the forward and…

Diffusion models have revolutionized generative tasks through high-fidelity outputs, yet flow matching (FM) offers faster inference and empirical performance gains. However, current foundation FM models are computationally prohibitive for…

Inverse problems governed by partial differential equations (PDEs) are crucial in science and engineering. They are particularly challenging due to ill-posedness, data sparsity, and the added complexity of irregular geometries. Classical…

We present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an…

Diffusion models have emerged as a dominant framework for generative modeling, but their mathematical foundations are often presented separately through diffusion probabilistic models, score-based modeling, stochastic differential…

Abstract Diffusion models have recently gained prominence as a novel category of generative models. Despite their success, these models face a notable drawback in terms of slow sampling speeds, requiring a high number of function…

Diffusion models have achieved significant progress in both image and video generation while still suffering from huge computation costs. As an effective solution, flow matching aims to reflow the diffusion process of diffusion models into…

We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a…

Accurate characterization of subsurface flow is critical for Carbon Capture and Storage (CCS) but remains challenged by the ill-posed nature of inverse problems with sparse observations. We present Function-space Decoupled Diffusion…

Despite Flow Matching and diffusion models having emerged as powerful generative paradigms for continuous variables such as images and videos, their application to high-dimensional discrete data, such as language, is still limited. In this…

Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are…

Vision-Language Latent Diffusion Models (LDMs) (Rombach et al., 2022) provide powerful generative priors for inverse problems. However, existing LDM-based inverse solvers typically require a large number of neural function evaluations…

Geophysical inverse problems are often ill-posed and admit multiple solutions. Conventional discriminative methods typically yield a single deterministic solution, which fails to model the posterior distribution, cannot generate diverse…

Denoising Diffusion Probabilistic Models (DDPMs) have established a new state-of-the-art in generative image synthesis, yet their deployment is hindered by significant computational overhead during inference, often requiring up to 1,000…