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Towards Identifiable Unsupervised Domain Translation: A Diversified Distribution Matching Approach
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Proves identifiability conditions for distribution-matching unsupervised domain translation via auxiliary-variable conditional distribution matching (DIMENSION), with an MPA elimination theory and experiments on MNIST/rotated MNIST, shoes, and CelebA-HQ/Bitmoji.
Problem
CycleGAN-style unsupervised domain translation via distribution matching is non-identifiable because measure-preserving automorphisms allow content-misaligned translations.
Approach
Match many conditional distribution pairs over auxiliary-variable-induced subdomains instead of entire domains; under a sufficiently diverse condition, no shared non-trivial MPA exists, so the ground-truth translation functions are identifiable.
Key results
- DIMENSION achieves LPIPS 0.29 on E to rS and 0.11 on M to rM, versus 0.43 and 0.34 for CycleGAN-Loss.
- FID on CelebA-HQ is 32.03 for the proposed method versus 36.71 for CycleGAN-Loss and 196.52 for CycleGAN.
- Theory: with sufficiently diverse conditionals, identifiability holds with probability at least 1 - rho^C(I,2); robust bound 2rL degrades linearly with violation r.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use diversified conditional distribution matching with auxiliary variables instead of the baseline approach | UDT · Edges → Rotated Shoes | LPIPS: 0.43 \pm 0.06 -> 0.29 $\pm$ 0.06 | Helped |
| Use diversified conditional distribution matching with auxiliary variables instead of the baseline approach | UDT · Rotated Shoes → Edges | LPIPS: 0.41 \pm 0.07 -> 0.35 $\pm$ 0.10 | Helped |
| Use diversified conditional distribution matching with auxiliary variables instead of the baseline approach | UDT · MNIST → Rotated MNIST | LPIPS: $0.25 \pm 0.09$ -> 0.11 $\pm$ 0.08 | Helped |
| Use diversified conditional distribution matching with auxiliary variables instead of the baseline approach | UDT · Rotated MNIST → MNIST | LPIPS: $ 0.25 \pm 0.09 $ -> 0.09 $\pm$ 0.04 | Helped |
| Use diversified conditional distribution matching with auxiliary variables instead of the strongest baseline | UDT · Edges | FID: 33.95 -> 21.47 | Helped |
| Use diversified conditional distribution matching with auxiliary variables instead of the strongest baseline | UDT · Rotated Shoes | FID: 55.42 -> 40.14 | Helped |
| Use diversified conditional distribution matching with auxiliary variables instead of the strongest baseline | UDT · MNIST | FID: 11.78 -> 13.95 | Hurt |
| Use diversified conditional distribution matching with auxiliary variables instead of the strongest baseline | UDT · Rotated MNIST | FID: 11.67 -> 16.07 | Hurt |
| Use diversified conditional distribution matching with auxiliary variables instead of the strongest baseline | UDT · CelebA-HQ | FID: 32.40 -> 32.03 | Helped |
| Use diversified conditional distribution matching with auxiliary variables instead of the strongest baseline | UDT · Bitmoji | FID: 27.59 -> 20.50 | Helped |
Surprising findings
- FID for U-GAT-IT (11.78) and the proposed method's MNIST-to-rotated-MNIST FID are not the best in all columns, and the proposed method is not best on FID for M, where U-GAT-IT scores lower.
Limitations
- Assumes deterministic, bijective ground-truth translation functions; multiple valid translations per content are not modeled.
- Requires auxiliary variables (e.g., labels or CLIP-annotated attributes), which may be nontrivial to obtain.
Experimental setup
Datasets: MNIST Edges2Shoes CelebA-HQ Bitmoji faces
Benchmarks: MNIST to rotated MNIST Edges to rotated shoes CelebA-HQ to Bitmoji
Metrics: LPIPS FID
Baselines: CycleGAN CycleGAN+Id MUNIT UNIT U-GAT-IT StarGAN-v2 Hneg-SRC GP-UNIT OverLORD ZeroDIM
Builds on: CycleGAN GAN
Closest papers by meaning
- Universal Multi-Domain Translation via Diffusion Routers (ICLR 2026 · similarity 0.88)
- Unsupervised Image-to-Image Translation Using Domain-Specific Variational Information Bound (NeurIPS 2018 · similarity 0.88)
- Domain Transfer Becomes Identifiable via a Single Alignment (ICML 2026 · similarity 0.88)
- Content-Style Learning from Unaligned Domains: Identifiability under Unknown Latent Dimensions (ICLR 2025 · similarity 0.87)
- Prompt-Based Distribution Alignment for Unsupervised Domain Adaptation (AAAI 2024 · similarity 0.86)
- AdvST: Revisiting Data Augmentations for Single Domain Generalization (AAAI 2024 · similarity 0.86)
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