TRACE: Transport Alignment Conformal Prediction via Diffusion and Flow Matching Models

TL;DR

TRACE introduces a novel conformal prediction method using transport alignment in diffusion and flow models, enabling valid, adaptive prediction regions for complex, multimodal outputs without likelihood evaluation.

Contribution

The paper proposes a transport-based nonconformity score for conformal prediction that works with diffusion and flow models, avoiding restrictive assumptions and likelihood computations.

Findings

Valid coverage achieved on synthetic and real datasets.

Prediction regions adapt to multimodal and non-convex distributions.

Scores are robust to computational budget variations.

Abstract

Constructing valid and informative conformal prediction regions for multi-dimensional outputs remains a fundamental challenge. While conformal prediction provides finite-sample, distribution-free coverage guarantees, its practical performance critically depends on the choice of nonconformity score. Existing approaches often rely on restrictive geometric assumptions or require explicit likelihood evaluation and invertible transformations, limiting their applicability in complex generative settings. In this work, we introduce TRACE (TRansport Alignment Conformal Estimation), a conformal prediction framework that defines nonconformity through transport alignment in diffusion and flow matching models. Rather than evaluating likelihoods, we measure how well a candidate output aligns with the learned generative dynamics by averaging denoising or velocity-matching errors along stochastic transport trajectories. The resulting transport-based scores are scalar-valued and can be calibrated using split conformal prediction, yielding valid marginal coverage under exchangeability. We further analyze the statistical properties of the proposed scores and their sensitivity to computational budget. Experiments on synthetic and real datasets demonstrate valid coverage and show that the resulting regions adapt naturally to multimodal and non-convex conditional distributions.