Content-Style Identification via Differential Independence

TL;DR

This paper introduces a new structural condition called content-style differential independence (CSDI) that enables the identification of content and style factors in generative models, even when they are dependent and the Jacobian is dense, facilitating tasks like domain transfer.

Contribution

The authors propose CSDI, a novel orthogonality-based condition for content-style disentanglement, and develop scalable training methods for high-dimensional generative models.

Findings

CSDI enables identifiability without independence assumptions.

The proposed method improves counterfactual generation and domain translation.

Experiments validate the theoretical analysis across multiple datasets.

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.