Related papers: D-Flow SGLD: Source-Space Posterior Sampling for S…

We propose a data-efficient, physics-aware generative framework in function space for inverse PDE problems. Existing plug-and-play diffusion posterior samplers represent physics implicitly through joint coefficient-solution modeling,…

Inverse medium scattering solvers generally reconstruct a single solution without an associated measure of uncertainty. This is true both for the classical iterative solvers and for the emerging deep learning methods. But ill-posedness and…

Stellar streams offer one of the most sensitive probes of the Milky Way`s gravitational potential, as their phase-space morphology encodes both the tidal field of the host galaxy and the internal structure of their progenitors. In this…

We provide a clear and concise introduction to the subjects of inverse problems and data assimilation, and their inter-relations. The first part of our notes covers inverse problems; this refers to the study of how to estimate unknown model…

We present a dual-guided framework for reconstructing unsteady incompressible flow fields using sparse observations. The approach combines optimized sensor placement with a physics-informed guided generative model. Sensor locations are…

Generative models excel at synthesizing high-fidelity samples from complex data distributions, but they often violate hard constraints arising from physical laws or task specifications. A common remedy is to project intermediate samples…

Efficient sampling of complex data distributions can be achieved using trained invertible flows (IF), where the model distribution is generated by pushing a simple base distribution through multiple non-linear bijective transformations.…

Existing generative models for time series forecasting often transform simple priors (typically Gaussian) into complex data distributions. However, their sampling initialization, independent of historical data, hinders the capture of…

Bayesian models based on Gaussian processes (GPs) offer a flexible framework to predict spatially distributed variables with uncertainty. But the use of nonstationary priors, often necessary for capturing complex spatial patterns, makes…

Machine Learning is beginning to provide state-of-the-art performance in a range of environmental applications such as streamflow prediction in a hydrologic basin. However, building accurate broad-scale models for streamflow remains…

Electrostatic generative models such as PFGM++ have recently emerged as a powerful framework, achieving state-of-the-art performance in image synthesis. PFGM++ operates in an extended data space with auxiliary dimensionality $D$, recovering…

Current discriminative depth estimation methods often produce blurry artifacts, while generative approaches suffer from slow sampling due to curvatures in the noise-to-depth transport. Our method addresses these challenges by framing depth…

The efficient resolution of Bayesian inverse problems remains challenging due to the high computational cost of traditional sampling methods. In this paper, we propose a novel framework that integrates Conditional Flow Matching (CFM) with a…

Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy and incomplete data or inherent non-uniqueness. A prominent example is full waveform inversion, which estimates Earth's subsurface…

The growing demand for text-to-image generation has led to rapid advances in generative modeling. Recently, text-to-image diffusion models trained with flow matching algorithms, such as FLUX, have achieved remarkable progress and emerged as…

Generative models have emerged as a powerful paradigm for solving physics systems and modeling complex spatiotemporal dynamics. However, achieving high physical accuracy without incurring high computational cost remains a fundamental…

Inverse scattering problems are critical in electromagnetic imaging and medical diagnostics but are challenged by their nonlinearity and diverse measurement scenarios. This paper proposes a physics-informed deep contrast source inversion…

In image processing, solving inverse problems is the task of finding plausible reconstructions of an image that was corrupted by some (usually known) degradation operator. Commonly, this process is done using a generative image model that…

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…

Flow Matching has recently emerged as a popular class of generative models for simulating a target distribution $\mu_1$ from samples drawn from a source distribution $\mu_0$. This framework relies on a fixed coupling between $\mu_0$ and…