Midpoint Generative Models

2026-05-28

AI Summary

This work proposes a single-step generative modeling paradigm grounded in midpoint symmetry. Addressing the lack of theoretical foundations in existing approaches, the authors leverage the symmetry inherent in linear interpolation within flow matching and identify that the drift field vanishes at the midpoint. Building on this property, they introduce midpoint divergence as a measure of distributional discrepancy and generalize it through random flipping and symmetric stochastic interpolation. This is the first method to incorporate midpoint symmetry into single-step generative models, offering both theoretical rigor and practical trainability. Experimental results demonstrate that the proposed model achieves performance on par with current state-of-the-art single-step generative methods across multiple benchmarks, confirming its effectiveness and competitiveness.

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.

Problem

• generative modeling
• one-step generation
• distribution discrepancy
• midpoint divergence
• flow matching

Innovation

• Midpoint Generative Models
• Flow Matching
• Midpoint Divergence
• One-step Generative Modeling
• Symmetric Stochastic Interpolants