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Midpoint Generative Models (MGM) are introduced as a novel framework for training one-step generative models, leveraging a symmetry in Flow Matching where the drift field vanishes at the midpoint ($t=1/2$) when endpoint distributions are identical. This vanishing drift field's norm defines the Midpoint Divergence, a valid discrepancy between distributions, which is then generalized using randomly flipped interpolations and symmetric stochastic interpolants. A variational formulation of this generalized divergence provides a tractable objective, leading to an effective MGM algorithm that achieves competitive performance against other one-step generative models.
A new generative modeling approach leverages the midpoint symmetry of Flow Matching to define a theoretically grounded and practically effective training objective for one-step generators.
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.