Mean Velocity Matching: Rethinking Generative Dynamics in Diffusion Models

Yunhong Zhang, Changjie Cao, Zhihua Zhang, Bingli Liu, Zongjie Cao +2

This work studies prediction parameterization for stochastic generative dynamics in diffusion models. Existing velocity-based generative models provide the simplicity of learning a single transport field, but their standard formulation is deterministic, whereas stochastic extensions generally require additional score information or an intermediate velocity-to-score reconstruction. To retain single-field prediction while directly supporting stochastic reverse dynamics, this paper introduces Mean Velocity Matching (MVM). MVM constructs a Gaussian perturbation process for which the conditional expectation of a restoration-oriented velocity, $(x_0-x_t)/t$, directly forms the reverse-SDE drift. Consequently, a single learned field is sufficient to parameterize the stochastic reverse process without separately estimating or reconstructing the score. Because direct regression of this velocity becomes unbounded near $t=0$, MVM further introduces a $\sqrt{t}$-scaled parameterization that preserves the reverse dynamics while yielding a bounded training target. The same learned field also induces a deterministic probability-flow ODE, enabling stochastic and deterministic sampling to be…