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.arXiv preprint arXiv:2410.03229, 2024
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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.
Flow learners parameterize transport vector fields to generate PDE trajectories through integration, offering a physics-to-physics organizing principle for learned solvers.
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
Flow learners parameterize transport vector fields to generate PDE trajectories through integration, offering a physics-to-physics organizing principle for learned solvers.
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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.