Equivariant Latent Alignment via Flow Matching under Group Symmetries

2026-05-28

AI Summary

Existing equivariant representation learning methods often compromise strict equivariance due to misalignment between the latent space and group actions. This work systematically identifies and addresses this issue for the first time by introducing a residual latent flow framework that dynamically corrects latent trajectories under group actions—such as those of SO(n)—via a flow-matching mechanism, thereby enforcing strict equivariance constraints on latent representations. By integrating continuous normalizing flows, group representation theory, and equivariant neural networks, the proposed method significantly reduces alignment errors across multiple benchmarks, leading to improved geometric consistency and visual fidelity in novel view synthesis.

Abstract

Geometry-aware generative models and novel view synthesis approaches have shown strong potential in 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 in novel view synthesis. However, we identify that existing approaches often suffer from latent misalignment, a discrepancy between the intended group action and the actually required transformations in the latent space. Consequently, the learned latents often fail to consistently preserve the equivariant relations imposed by the underlying group symmetry. To address this, we propose Residual Latent Flow, a flow-based framework that corrects the misaligned latents, thereby improving compliance with the underlying equivariance relation. Our comprehensive experiments show that our method significantly reduces latent misalignment and improves novel view synthesis quality, under rotation groups SO(n).

Problem

• equivariance
• latent alignment
• group symmetries
• novel view synthesis
• geometric structure

Innovation

• equivariant representation learning
• latent alignment
• flow matching
• group symmetries
• novel view synthesis