Generative Inverse Design with Abstention via Diagonal Flow Matching

arXiv cs.LG / 3/18/2026

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Key Points

The authors propose Diagonal Flow Matching (Diag-CFM) to fix instability in inverse-design training caused by arbitrary ordering and scaling of design parameters and labels.
Diag-CFM uses a zero-anchoring strategy that pairs design coordinates with noise and labels with zero, making the learning objective invariant to coordinate permutations.
The method achieves order-of-magnitude improvements in round-trip design-performance accuracy compared with standard conditional flow matching and invertible neural networks for design dimensions up to P=100, validated on airfoil, gas turbine combustor, and an analytical benchmark.
The paper introduces two uncertainty metrics, Zero-Deviation and Self-Consistency, enabling selecting the best candidate among generations, abstaining from unreliable predictions, and detecting out-of-distribution targets, outperforming ensembles and general-purpose baselines.
This work demonstrates scalable generative inverse design with abstention in practical engineering tasks.

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.