Midpoint Generative Models

Daniil Shlenskii, Nikita Gushchin, Lev Novitskiy, Dmitry V. Dylov, Alexander Korotin

Keywords: Generative Models

Abstract: We introduce *Midpoint Generative Models* (MGM), a principled framework for training one-step generative models. MGM is based on a simple symmetry of Flow Matching with linear interpolation: when the two endpoint distributions coincide, the corresponding drift field vanishes at the midpoint time, $t=1/2$. We show that the norm of this field defines a valid discrepancy between distributions, which we call the *Midpoint Divergence*. We extend this discrepancy beyond the midpoint by introducing randomly flipped interpolations and further generalize it by replacing deterministic linear Flow Matching interpolations with symmetric stochastic interpolants, yielding a generalized Midpoint Divergence. Finally, we derive a variational formulation of our generalized divergence, yielding a tractable objective for training a one-step generator. The resulting MGM algorithm offers an effective and theoretically grounded approach to generative modeling, achieving competitive performance against existing one-step generative modeling methods.

Submission Number: 115