Generative Inverse Design with Abstention via Diagonal Flow Matching

TL;DR

This paper introduces Diagonal Flow Matching, a stable generative inverse design method that improves accuracy and enables uncertainty-based abstention for complex design problems.

Contribution

We propose Diagonal Flow Matching with a zero-anchoring strategy, providing invariance to coordinate permutations and significantly enhancing inverse design stability and accuracy.

Findings

Order-of-magnitude improvement in round-trip accuracy over CFM.

Effective uncertainty metrics for candidate selection and out-of-distribution detection.

Validated on airfoil, gas turbine, and analytical benchmarks.

Abstract

Inverse design aims to find design parameters $x$ achieving target performance $y^*$. Generative approaches learn bidirectional mappings between designs and labels, enabling diverse solution sampling. However, standard conditional flow matching (CFM), when adapted to inverse problems by pairing labels with design parameters, exhibits strong sensitivity to their arbitrary ordering and scaling, leading to unstable training. We introduce Diagonal Flow Matching (Diag-CFM), which resolves this through a zero-anchoring strategy that pairs design coordinates with noise and labels with zero, making the learning problem provably invariant to coordinate permutations. This yields order-of-magnitude improvements in round-trip accuracy over CFM and invertible neural network baselines across design dimensions up to $P{=}100$. We develop two architecture-intrinsic uncertainty metrics, Zero-Deviation and Self-Consistency, that enable three practical capabilities: selecting the best candidate among multiple generations, abstaining from unreliable predictions, and detecting out-of-distribution targets; consistently outperforming ensemble and general-purpose alternatives across all tasks. We validate on airfoil, gas turbine combustor, and an analytical benchmark with scalable design dimension.