相关论文: Physics-Informed Generative Solver: Bridging Data-…

Score-based generative models (SGMs) synthesize new data samples from Gaussian white noise by running a time-reversed Stochastic Differential Equation (SDE) whose drift coefficient depends on some probabilistic score. The discretization of…

Deep learning paradigms, such as PINNs and neural operators, have significantly advanced the solving of PDEs. However, they often struggle to capture the continuous integral nature of physical systems, relying either on pointwise residuals…

Score-based generative modeling (SGM) is a highly successful approach for learning a probability distribution from data and generating further samples. We prove the first polynomial convergence guarantees for the core mechanic behind SGM:…

We propose a new method for inferring the governing stochastic ordinary differential equations (SODEs) by observing particle ensembles at discrete and sparse time instants, i.e., multiple "snapshots". Particle coordinates at a single time…

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift…

Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth's highly heterogeneous structure is unknown, present a…

Score-based generative models (SGMs) have recently emerged as a promising class of generative models. However, a fundamental limitation is that their sampling process is slow due to a need for many (e.g., 2000) iterations of sequential…

Generative models have emerged as powerful priors for solving inverse problems. These models typically represent a class of natural signals using a single fixed complexity or dimensionality. This can be limiting: depending on the problem, a…

Data assimilation and scientific inverse problems require reconstructing high-dimensional physical states from sparse and noisy observations, ideally with uncertainty-aware posterior samples that remain faithful to learned priors and…

Recent advances in generative AI offer promising solutions for synthetic data generation but often rely on large datasets for effective training. To address this limitation, we propose a novel generative model that learns from limited data…

While score based generative models, or diffusion models, have found success in image synthesis, they are often coupled with text data or image label to be able to manipulate and conditionally generate images. Even though manipulation of…

We introduce a physics-informed neural framework for modeling static and time-dependent galactic gravitational potentials. The method combines data-driven learning with embedded physical constraints to capture complex, small-scale features…

We address tracking and prediction of multiple moving objects in visual data streams as inference and sampling in a disentangled latent state-space model. By encoding objects separately and including explicit position information in the…

Score-based diffusion models generate samples from a complex underlying data distribution by time-reversal of a diffusion process and represent the state-of-the-art in many generative AI applications. Here, I show how a generative diffusion…

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…

We propose a generative model that can infer a distribution for the underlying spatial signal conditioned on sparse samples e.g. plausible images given a few observed pixels. In contrast to sequential autoregressive generative models, our…

Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…

Conventional wisdom suggests that autoregressive models are used to process discrete data. When applied to continuous modalities such as visual data, Visual AutoRegressive modeling (VAR) typically resorts to quantization-based approaches to…

Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…

Score-based diffusion models are a powerful class of generative models, widely utilized across diverse domains. Despite significant advancements in large-scale tasks such as text-to-image generation, their application to constrained domains…