Content-Style Identification via Differential Independence

2026-05-18

AI Summary

This work addresses the challenge of disentangling content and style from nonlinearly mixed observations in unpaired multi-domain data. It proposes a Content-Style Differential Independence (CSDI) condition, which enforces that infinitesimal variations in content and style induce orthogonal directions on the data manifold, thereby ensuring identifiability even when the two factors are statistically dependent and their Jacobian is dense. Departing from conventional assumptions that rely on statistical independence or sparse Jacobians, the method introduces a block-orthogonality constraint based on numerical Jacobian approximation together with stochastic regularization, making it suitable for high-dimensional generative models. Theoretical identifiability is empirically validated, and the approach demonstrates significant improvements over existing methods in counterfactual generation and domain translation tasks.

Abstract

Generative analysis often models multi-domain observations as nonlinear mixtures of domain-invariant content variables and domain-specific style variables. Identifying both factors from unpaired domains enables tasks such as domain transfer and counterfactual data generation. Prior work establishes identifiability under (block-wise) statistical independence between content and style, or via sparse Jacobian assumptions on the nonlinear mixing function, but such conditions can be restrictive in practice. In this work, we introduce content-style differential independence (CSDI), an alternative structural condition requiring that infinitesimal variations in content and style induce orthogonal directions on the data manifold, thereby enabling identifiability even when content and style are dependent and the Jacobian is dense. We operationalize this condition through a blockwise orthogonality constraint on the Jacobian subspaces associated with content and style. To support high-dimensional generative models, we design a stochastic regularizer based on numerical Jacobian approximation, enabling scalable training in settings such as high-resolution image generation. Experiments across multiple datasets corroborate the identifiability analysis and demonstrate practical benefits on counterfactual generation and domain translation.

Problem

• content-style disentanglement
• identifiability
• nonlinear mixing
• domain transfer
• counterfactual generation

Innovation

• differential independence
• content-style disentanglement
• Jacobian orthogonality
• identifiability
• counterfactual generation