Related papers: Malliavin Calculus for Score-based Diffusion Model…
Diffusion models have achieved great success in generating high-dimensional samples across various applications. While the theoretical guarantees for continuous-state diffusion models have been extensively studied, the convergence analysis…
We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models,…
The stochastic partial differential equation analyzed in this work, is motivated by a simplified mesoscopic physical model for phase separation. It describes pattern formation due to adsorption and desorption mechanisms involved in surface…
We introduce a general framework for approximating parabolic Stochastic Partial Differential Equations (SPDEs) based on fluctuation-dissipation balance. Using this approach we formulate Stochastic Discontinuous Galerkin Methods (SDGM). We…
It is well known that training a denoising score-based diffusion models requires tens of thousands of epochs and a substantial number of image data to train the model. In this paper, we propose to increase the efficiency in training…
Score-based diffusion models, while achieving remarkable empirical performance, often suffer from low sampling speed, due to extensive function evaluations needed during the sampling phase. Despite a flurry of recent activities towards…
Diffusion models, typically formulated as discretizations of stochastic differential equations (SDEs), have achieved state-of-the-art performance in generative tasks. However, their theoretical analysis often involves complex proofs. In…
This paper investigates the pricing of financial derivatives and the calculation of their delta Greek when the underlying asset is a jump-diffusion process in which the stochastic intensity component follows the CIR process. Utilizing…
This paper investigates the score-based diffusion models for density estimation when the target density admits a factorizable low-dimensional nonparametric structure. To be specific, we show that when the log density admits a $d^*$-way…
Inverse problems are ubiquitous because they formalize the integration of data with mathematical models. In many scientific applications the forward model is expensive to evaluate, and adjoint computations are difficult to employ; in this…
Building on recent advances in scientific machine learning and generative modeling for computational fluid dynamics, we propose a conditional score-based diffusion model designed for multi-scenarios fluid flow prediction. Our model…
Generative modeling has drawn much attention in creative and scientific data generation tasks. Score-based Diffusion Models, a type of generative model that iteratively learns to denoise data, have shown state-of-the-art results on tasks…
We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setting is notoriously challenging due to the intractability of…
Distribution matching (DM) is a versatile domain-invariant representation learning technique that has been applied to tasks such as fair classification, domain adaptation, and domain translation. Non-parametric DM methods struggle with…
By using the Malliavin calculus and finite jump approximations, the Driver-type integration by parts formula is established for the semigroup associated to stochastic (partial) differential equations with noises containing a subordinate…
This paper studies the original discrete-time denoising diffusion probabilistic model (DDPM) from a probabilistic point of view. We present three main theoretical results. First, we show that the time-dependent score function associated…
Diffusion generative modelling (DGM) based on stochastic differential equations (SDEs) with score matching has achieved unprecedented results in data generation. In this paper, we propose a novel fast high-quality generative modelling…
In this paper we introduce a new technique to construct unique strong solutions of SDEs with singular coefficients driven by certain Levy processes. Our method which is based on Malliavin calculus does not rely on a pathwise uniqueness…
By using the Malliavin calculus and finite-jump approximations, the Driver-type integration by parts formula is established for the semigroup associated to stochastic differential equations with noises containing a subordinate Brownian…
A class of implicit Milstein type methods is introduced and analyzed in the present article for stochastic differential equations (SDEs) with non-globally Lipschitz drift and diffusion coefficients. By incorporating a pair of method…