Related papers: Stochastic quantization and diffusion models

Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…

Controlling memorization in diffusion models is critical for applications that require generated data to closely match the training distribution. Existing approaches mainly focus on data centric or model centric modifications, treating the…

We provide an overview of the diffusion model as a method to generate new samples. Generative models have been recently adopted for tasks such as art generation (Stable Diffusion, Dall-E) and text generation (ChatGPT). Diffusion models in…

We present a deep learning model, DE-LSTM, for the simulation of a stochastic process with an underlying nonlinear dynamics. The deep learning model aims to approximate the probability density function of a stochastic process via numerical…

The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…

Although the governing equations of many systems, when derived from first principles, may be viewed as known, it is often too expensive to numerically simulate all the interactions they describe. Therefore researchers often seek simpler…

Imitation learning with diffusion models has advanced robotic control by capturing the multi-modal action distributions. However, existing methods typically treat observations only as high-level conditions to the denoising network, rather…

Stochastic differential equations (SDEs) are one of the most important representations of dynamical systems. They are notable for the ability to include a deterministic component of the system and a stochastic one to represent random…

We develop a novel approach towards causal inference. Rather than structural equations over a causal graph, we learn stochastic differential equations (SDEs) whose stationary densities model a system's behavior under interventions. These…

In this article we show that a finite dimensional stochastic differential equation driven by a L\'evy process can be formulated as a stochastic partial differential equation. We prove the existence and uniqueness of strong solutions of such…

Along with recent diffusion models, randomized smoothing has become one of a few tangible approaches that offers adversarial robustness to models at scale, e.g., those of large pre-trained models. Specifically, one can perform randomized…

Because diffusion models have shown impressive performances in a number of tasks, such as image synthesis, there is a trend in recent works to prove (with certain assumptions) that these models have strong approximation capabilities. In…

Spatially distributed problems are often approximately modelled in terms of partial differential equations (PDEs) for appropriate coarse-grained quantities (e.g. concentrations). The derivation of accurate such PDEs starting from finer…

We consider an SDE in R^m of the type dX(t)=a(X(t))dt+dU(t) with a L\'evy process U and study the problem for the distribution of a solution to be regular in various senses. We do not impose any specific conditions on the L\'evy measure of…

Derivation of the probability density evolution provides invaluable insight into the behavior of many stochastic systems and their performance. However, for most real-time applica-tions, numerical determination of the probability density…

In this study, a new coupled Partial Differential Equation (CPDE) based image denoising model incorporating space-time regularization into non-linear diffusion is proposed. This proposed model is fitted with additive Gaussian noise which…

Denoising diffusion models represent a recent emerging topic in computer vision, demonstrating remarkable results in the area of generative modeling. A diffusion model is a deep generative model that is based on two stages, a forward…

This paper gives direct derivations of the differential equations and likelihood formulas of diffusion models assuming only knowledge of Gaussian distributions. A VAE analysis derives both forward and backward stochastic differential…

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…

Numerical approximation of the long time behavior of a stochastic differential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical…