Flowing with Confidence

TL;DR

The paper introduces Flow Matching with Confidence (FMwC), a method that provides per-sample confidence scores for generative models by propagating input-dependent noise through the network, enhancing trust and interpretability.

Contribution

FMwC is a novel approach that injects input-dependent noise and propagates its variance in closed form to estimate confidence at standard sampling costs, enabling improved filtering, editing, and adaptive sampling.

Findings

Confidence scores correlate with divergence of the learned velocity field.

Filtering improves image quality and crystal stability.

Rewinding trajectories helps identify model commitment points.

Abstract

Generative models can produce nonsensical text, unrealistic images, and unstable materials faster than simulation or human review can absorb; without per-sample confidence, trust erodes. Existing fixes run $k$ ensembles or stochastic trajectories at $k\times$ compute, measuring variability between models, not model confidence. We propose Flow Matching with Confidence (FMwC). FMwC injects input-dependent multiplicative noise at selected layers, propagates its variance through the network in closed form, and integrates it along the ODE trajectory, yielding a per-sample confidence score at standard sampling cost. The score supports multiple uses: filtering improves image quality and thermodynamic stability of crystals; editing rewinds trajectories to the points where the model commits and redirects them; and adaptive stepping concentrates ODE compute where the flow is ambiguous. We find that the confidence score correlates with the magnitude of the divergence of the learned velocity field, which gives us a window to understand the generative process, opening up surgical forms of guidance that target the moments that matter, new sampling algorithms and interpretability of generative models.