Diffusion models learn a velocity field that matches the Wasserstein gradient flow of the OU process, not a true score, and errors in the Stein null space leave density transport exact.
Reverse-time diffusion equation models
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Are We Really Learning the Score Function? Reinterpreting Diffusion Models Through Wasserstein Gradient Flow Matching
Diffusion models learn a velocity field that matches the Wasserstein gradient flow of the OU process, not a true score, and errors in the Stein null space leave density transport exact.