Föllmer processes are variationally optimal among generative diffusions because they minimize the impact of drift estimation error on path-space KL divergence, rendering different interpolation schedules statistically equivalent.
Schrödinger-Föllmer sampler: sampling without ergodicity
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Derives that the conditional terminal law of the optimal controlled process is a Gibbs measure on a proximally penalized energy, giving potential, averaged-gradient, and barycentric drift formulas with terminal-time gradient recovery and low-temperature global-minimizer attraction.
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Variational Optimality of F\"ollmer Processes in Generative Diffusions
Föllmer processes are variationally optimal among generative diffusions because they minimize the impact of drift estimation error on path-space KL divergence, rendering different interpolation schedules statistically equivalent.
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Optimal drift optimizer for non-convex optimization
Derives that the conditional terminal law of the optimal controlled process is a Gibbs measure on a proximally penalized energy, giving potential, averaged-gradient, and barycentric drift formulas with terminal-time gradient recovery and low-temperature global-minimizer attraction.
- The Ensemble Schr{\"o}dinger Bridge filter for Nonlinear Data Assimilation