Wei Deng

Thought is only a flash in the middle of a long night. But this flash means everything.

Raymond Poincaré

Flow Matching and Stochastic Interpolant


The Triangle of Flow, Diffusion, and PDE

Connections between Probability Flows, Diffusions, and PDEs.

Coupling by Reflection (II)

A general coupling technique for characterizing a broad range of diffusions.

Girsanov and MLE

An application of Girsanov theorem in parameter estimation.

Schrödinger Bridge Problem

A framework that unifies optimal transport, FB-SDEs, fluid dynamics, and stochastic control.

Hamiltonian Monte Caro

An elegant sampler that utilizes Hamiltonian dynamics to propose new states in simulations.

Couplings and Monte Carlo Methods (I)

A family of techniques to understand the convergence of random variables.

The Lyapunov Function Method for Poincaré Inequality

An elegant functional inequality that unifies ODEs, PDEs, SDEs, functional analysis, and Riemannian geometry.

Replica Exchange and Variance Reduction

Running multiple MCMCs at different temperatures to explore the solution thoroughly.

Dynamic Importance Sampling and Beyond

The most promising sampling framework for multi-modal simulations.