Related papers: Generating solution paths of Markovian stochastic …

We address the problem of simulation and parameter inference for chemical reaction networks described by the chemical Langevin equation, a stochastic differential equation (SDE) representation of the dynamics of the chemical species. This…

Diffusion models excel at capturing the natural design spaces of images, molecules, DNA, RNA, and protein sequences. However, rather than merely generating designs that are natural, we often aim to optimize downstream reward functions while…

In this paper, we consider stochastic versions of three classical growth models given by ordinary differential equations (ODEs). Indeed we use stochastic versions of Von Bertalanffy, Gompertz, and Logistic differential equations as models.…

Diffusion models recently developed for generative AI tasks can produce high-quality samples while still maintaining diversity among samples to promote mode coverage, providing a promising path for learning stochastic closure models.…

The optimization of the latents and parameters of diffusion models with respect to some differentiable metric defined on the output of the model is a challenging and complex problem. The sampling for diffusion models is done by solving…

Diffusion models have been achieving state-of-the-art results across various generation tasks. However, a notable drawback is their sequential generation process, requiring long-sequence step-by-step generation. Existing methods, such as…

Score-based Generative Models (SGMs) have demonstrated exceptional synthesis outcomes across various tasks. However, the current design landscape of the forward diffusion process remains largely untapped and often relies on physical…

Sampling from Diffusion Models can alternatively be seen as solving differential equations, where there is a challenge in balancing speed and image visual quality. ODE-based samplers offer rapid sampling time but reach a performance limit,…

A popular approach to sample a diffusion-based generative model is to solve an ordinary differential equation (ODE). In existing samplers, the coefficients of the ODE solvers are pre-determined by the ODE formulation, the reverse discrete…

This paper explores the application of Stochastic Differential Equations (SDE) to interpret the text generation process of Large Language Models (LLMs) such as GPT-4. Text generation in LLMs is modeled as a stochastic process where each…

Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…

Learning the underlying distribution of molecular graphs and generating high-fidelity samples is a fundamental research problem in drug discovery and material science. However, accurately modeling distribution and rapidly generating novel…

We provide theoretical convergence guarantees for score-based generative models (SGMs) such as denoising diffusion probabilistic models (DDPMs), which constitute the backbone of large-scale real-world generative models such as DALL$\cdot$E…

In applications of diffusion models, controllable generation is of practical significance, but is also challenging. Current methods for controllable generation primarily focus on modifying the score function of diffusion models, while Mean…

In this article we study (possibly degenerate) stochastic differential equations (SDE) with irregular (or discontiuous) coefficients, and prove that under certain conditions on the coefficients, there exists a unique almost everywhere…

Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given…

In this article, we consider McKean stochastic differential equations, as well as their corresponding McKean-Vlasov partial differential equations, which admit a unique stationary state, and we study the linearized It\^o diffusion process…

A new class of stochastic field models is constructed using nested stochastic partial differential equations (SPDEs). The model class is computationally efficient, applicable to data on general smooth manifolds, and includes both the…

Turbulent flows have historically presented formidable challenges to predictive computational modeling. Traditional numerical simulations often require vast computational resources, making them infeasible for numerous engineering…

In recent years, diffusion models (DMs) have become a popular method for generating synthetic data. By achieving samples of higher quality, they quickly became superior to generative adversarial networks (GANs) and the current…