CompFlow: Composing Velocity Fields for Multi-Condition Generation

Luca Miglior, Vincenzo Gervasi, Davide Bacciu

Keywords: flow matching, compositional generation, product of experts

TL;DR: We present CompFlow, a compositional generation framework that proves velocity addition in flow matching implements a Product-of-Experts composition, enabling joint control over multiple conditions at inference time via a standard ODE solver.

Abstract:

Generating samples that satisfy many conditions simultaneously can be achieved with a surprisingly simple operation: summing conditional velocity fields at inference time. We introduce CompFlow, a flow-matching framework that enables fully compositional inference without retraining, architectural changes, or specialized samplers. We show that velocity addition implements a Product of Experts composition, extending classifier-free guidance to arbitrarily many conditions. On CLEVR, a single-object-conditioned model is composed at inference to simultaneously control shape, color, and position for up to five objects, achieving 99.1--86.5\% per-object accuracy with 30× fewer network evaluations than prior baselines. On high-resolution images, CompFlow satisfies up to five conditions simultaneously and substantially outperforms state-of-the-art single-prompt composition.
We believe compositional generation can become a standard inference-time capability to control complex generation scenarios.

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Submission Number: 37