First-Order Stationarity of Reverse Diffusions
Reverse-time SDE samplers get explicit first-order stationarity guarantees under convex noising potentials.
The paper builds a first-order theory connecting diffusion sampling with optimization guarantees. It says reverse-time overdamped and underdamped Langevin SDE flows contract relative Fisher divergences at exponential rates when the forward process uses a strongly convex stationary potential. The authors argue this advantage is specific to SDE-based reverse diffusion, not ODE reverse processes. With discretization included, they prove averaged stationarity bounds for both sampler types, but note the certificate is local: it checks score consistency, not global mode weights. ArXiv · AI/CL/LG's note
The paper builds a first-order theory connecting diffusion sampling with optimization guarantees. It says reverse-time overdamped and underdamped Langevin SDE flows contract relative Fisher divergences at exponential rates when the forward process uses a strongly convex stationary potential. The authors argue this advantage is specific to SDE-based reverse diffusion, not ODE reverse processes. With discretization included, they prove averaged stationarity bounds for both sampler types, but note the certificate is local: it checks score consistency, not global mode weights. ArXiv · AI/CL/LG's note
score 4