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.
Elucidating the design choice of probability paths in flow matching for forecasting
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Empirical flow matching introduces coupled biases from plug-in estimation, including altered statistical targets, non-gradient minimizers, and non-unique dynamics via flux-null fields, with base distribution controlling kinetic energy tails.
Learned PDE solving should target transport over admissible futures via flow learners, not snapshot state regression.
Stronger physics priors in neural networks for spatio-temporal shear flow forecasting yield substantially lower training carbon footprints than weak or no priors, though inference savings are less consistent.
citing papers explorer
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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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On The Hidden Biases of Flow Matching Samplers
Empirical flow matching introduces coupled biases from plug-in estimation, including altered statistical targets, non-gradient minimizers, and non-unique dynamics via flux-null fields, with base distribution controlling kinetic energy tails.
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Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing
Learned PDE solving should target transport over admissible futures via flow learners, not snapshot state regression.
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Physics Priors Offer Useful Accuracy-Carbon Trade-Offs in Spatio-Temporal Forecasting
Stronger physics priors in neural networks for spatio-temporal shear flow forecasting yield substantially lower training carbon footprints than weak or no priors, though inference savings are less consistent.