First-Order Stationarity of Reverse Diffusions
Recent literature has shown a strong connection between optimization and sampling. We develop the corresponding first-order theory for diffusion models. First, the SDE-based reverse-time flows of overdamped and underdamped Langevin diffusions contract relative Fisher divergences at explicit exponential rates whenever the stationary potential of the forward process is strongly convex---a condition on the noising process one chooses, not on the data. This is a unique advantage of SDE-based reverse diffusion, absent in the reverse process based on ODEs. Second, we incorporate discretization and establish averaged first-order stationarity bounds---the sampling analog of averaged gradient-norm...
| Authors | Zhifeng Chen, Chenyang Jiang, Yazhen Wang |
|---|---|
| Primary category | stat.ML |
| Published | 25 September 2026 |
| Last updated at source | 25 September 2026 |
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