Midpoint Generative Models

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.