Equivariant Latent Alignment via Flow Matching under Group Symmetries

Sunghyun Kim, Jaehoon Hahm, Jeongwoo Shin, Joonseok Lee

Keywords: Equivariant Representation Learning, Flow matching, Latent Correction, Latent Misalignment, Symmetry Group

TL;DR: We propose Residual Latent Flow, a flow-based correction method that fixes misaligned latents for more effective equivariant representation learning.

Abstract:

Geometry-aware generative models and novel view synthesis approaches have shown strong potential to improve visual fidelity and consistency. In parallel, equivariant representation learning has emerged as a powerful framework for constructing latent spaces where analytically known group transformations could act directly, capturing geometric structure in data and enhancing both interpretability and generalization.
However, we identify that existing approaches often suffer from \textit{latent misalignment}, a discrepancy between the intended group action and the actual required transformations in latent space, as the learned latents fail to consistently preserve the equivariant relations imposed by the underlying group symmetry. This misalignment degrades view synthesis quality and undermines the theoretical guarantees of equivariant representation learning.
To address this issue, we introduce \textbf{Residual Latent Flow}, a flow-matching-based correction framework that corrects the misaligned latents, thereby improving compliance with the underlying equivariance relation.
We show experiments that flow-based correction significantly reduces latent misalignment and improves novel view synthesis quality, under orthogonal group $\mathrm{SO}(n)$, using synthetic image datasets with rotational freedom. Our method demonstrates the efficacy of combining flow-based correction with equivariant representation learning, resulting in a new powerful framework for learning a more consistent and accurate group symmetry-aware models.

Primary Area: generative models

Submission Number: 2951