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Content-Style Learning from Unaligned Domains: Identifiability under Unknown Latent Dimensions
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Proves content-style identifiability from unaligned multi-domain data via cross-domain latent distribution matching, removing element-wise independence and the need for known latent dimensions (using sparsity), and implements it as a sparsity-regularized multi-domain GAN built on StyleGAN2-ADA.
Problem
Identifying content and style latent variables from unaligned multi-domain data under stringent conditions (element-wise independence, many domains, known latent dimensions).
Approach
Cross-domain latent distribution matching with block independence between content and style; sparsity penalty on style encoders lets over-estimated latent dimensions be used without loss of identifiability; reformulated as a multi-domain GAN with coupled latents, avoiding latent-domain DM modules.
Key results
- On AFHQ, the proposed method reaches FID 6.19 vs 6.28 for I-GAN, and style diversity 0.50 vs 0.16 for I-GAN.
- For translation on AFHQ, the proposed method attains FID 13.74 vs 16.83 for StarGANv2 and 27.36 hours training vs 96.99 hours total for I-GAN (Tr).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the proposed sparsity-regularized content-style model instead of I-GAN | AFHQ data generation · AFHQ | Style Diversity: 0.16 $\pm$ 0.02 -> 0.50 $\pm$ 0.03 | Helped |
| Use the proposed sparsity-regularized content-style model instead of I-GAN | CelebA-HQ data generation · CelebA-HQ | Style Diversity: 0.07 $\pm$ 0.03 -> 0.36 $\pm$ 0.04 | Helped |
| Use the proposed sparsity-regularized content-style model instead of I-GAN | CelebA-7 data generation · CelebA-7 | Style Diversity: 0.07 $\pm 0.03$ -> 0.26 $\pm$ 0.06 | Helped |
| Use the proposed model instead of I-GAN | AFHQ data generation · AFHQ | FID: 6.28 -> 6.19 | Helped |
| Use the proposed model instead of StyleGAN-ADA | CelebA-HQ data generation · CelebA-HQ | FID: 5.89 -> 5.70 | Helped |
| Use the proposed model instead of I-GAN | CelebA-7 data generation · CelebA-7 | FID: 5.18 -> 5.27 | Hurt |
| Use the proposed model instead of StarGANv2 | AFHQ translation · AFHQ translation | FID: 16.83 -> 13.74 | Helped |
| Use the proposed model instead of StarGANv2 | CelebA-HQ translation · CelebA-HQ translation | FID: 13.67 -> 16.61 | Hurt |
| Use the proposed model instead of I-GAN (Tr) | AFHQ translation · AFHQ translation | Training time (hours), Total: 96.99 -> 27.36 | Helped |
| Remove sparsity regularization (ablation) | Proposed content-style model · AFHQ content-style generation | content and style diversity | Hurt |
| Use the GAN-based implementation rather than direct latent distribution matching | Proposed content-style model · Image generation and translation | training time | Helped |
Surprising findings
- Without sparsity regularization the learned content collapses to a constant with all information captured by the style part.
Limitations
- Only sufficient, not necessary, identifiability conditions are established.
- Restricted to homogeneous continuous modalities such as images; discrete data like text not covered.
- GAN-based implementation is known to be unstable during training.
Experimental setup
Datasets: AFHQ CelebA-HQ CelebA
Benchmarks: AFHQ CelebA-HQ CelebA-7
Metrics: FID style diversity (LPIPS) training time
Baselines: I-GAN StyleGAN-ADA Transitional-cGAN StarGANv2 SmoothGAN
Builds on: StyleGAN2-ADA nonlinear ICA I-GAN
Closest papers by meaning
- Towards Identifiable Unsupervised Domain Translation: A Diversified Distribution Matching Approach (ICLR 2024 · similarity 0.87)
- Identifying Metric Structures of Deep Latent Variable Models (ICML 2025 · similarity 0.86)
- Unsupervised Disentanglement of Content and Style via Variance-Invariance Constraints (ICLR 2025 · similarity 0.85)
- A General Representation-Based Approach to Multi-Source Domain Adaptation (ICML 2025 · similarity 0.85)
- StyDeSty: Min-Max Stylization and Destylization for Single Domain Generalization (ICML 2024 · similarity 0.85)
- Concept Modulation Models: A Unified Framework for Identifiability and Extrapolation (NeurIPS 2026 · similarity 0.85)
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