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.
Physics-aware generative models for turbulent fluid flows through energy-consistent stochastic interpolants
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A discrete-time energy-conserving neural map with FDT-derived causal regularization reproduces stationary statistics and forced responses of CdV and Lorenz-96 turbulence from unperturbed data alone.
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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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Physics constraints and response validation in discrete-time reduced-order modeling: from idealized turbulent systems to climate dynamics
A discrete-time energy-conserving neural map with FDT-derived causal regularization reproduces stationary statistics and forced responses of CdV and Lorenz-96 turbulence from unperturbed data alone.