Related papers: Score-based Continuous-time Discrete Diffusion Mod…
Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by…
In Diffusion Probabilistic Models (DPMs), the task of modeling the score evolution via a single time-dependent neural network necessitates extended training periods and may potentially impede modeling flexibility and capacity. To counteract…
In Score based Generative Modeling (SGMs), the state-of-the-art in generative modeling, stochastic reverse processes are known to perform better than their deterministic counterparts. This paper delves into the heart of this phenomenon,…
Inverse problems describe the process of estimating the causal factors from a set of measurements or data. Mapping of often incomplete or degraded data to parameters is ill-posed, thus data-driven iterative solutions are required, for…
As a class of generative artificial intelligence frameworks inspired by statistical physics, diffusion models have shown extraordinary performance in synthesizing complicated data distributions through a denoising process gradually guided…
The ensemble-averaged dynamics of open quantum systems are typically irreversible. We show that this irreversibility need not hold at the level of individually monitored quantum trajectories. Our main results are analytical stochastic…
Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane-mediated receptor dynamics on cell surfaces, we…
The distortion-perception (DP) tradeoff reveals a fundamental conflict between distortion metrics (e.g., MSE and PSNR) and perceptual quality. Recent research has increasingly concentrated on evaluating denoising algorithms within the DP…
We study variance reduction for score estimation and diffusion-based sampling in settings where the clean (target) score is available or can be approximated. Starting from the Target Score Identity (TSI), which expresses the noisy marginal…
Score-based diffusion models are a powerful class of generative models, but their practical use often depends on training neural networks to approximate the score function. Training-free diffusion models provide an attractive alternative by…
Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…
We derive a general change of variables formula for score functions, showing that for a smooth, invertible transformation $\mathbf{y} = \phi(\mathbf{x})$, the transformed score function $\nabla_{\mathbf{y}} \log q(\mathbf{y})$ can be…
Generative diffusion models synthesize new samples by reversing a diffusive process that converts a given data set to generic noise. This is accomplished by training a neural network to match the gradient of the log of the probability…
Multi-target detection (MTD) is the problem of estimating an image from a large, noisy measurement that contains randomly translated and rotated copies of the image. Motivated by the single-particle cryo-electron microscopy technology, we…
We present a novel method for training score-based generative models which uses nonlinear noising dynamics to improve learning of structured distributions. Generalizing to a nonlinear drift allows for additional structure to be incorporated…
We present SURE-Score: an approach for learning score-based generative models using training samples corrupted by additive Gaussian noise. When a large training set of clean samples is available, solving inverse problems via score-based…
Deep Gaussian processes (DGPs) provide a robust paradigm for Bayesian deep learning. In DGPs, a set of sparse integration locations called inducing points are selected to approximate the posterior distribution of the model. This is done to…
In this note we prove sharp lower error bounds for numerical methods for jump-diffusion stochastic differential equations (SDEs) with discontinuous drift. We study the approximation of jump-diffusion SDEs with non-adaptive as well as…