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Can Diffusion Models Disentangle? A Theoretical Perspective
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Gives a learning-theoretic framework showing diffusion models can achieve approximate (ε,ν)-disentanglement and editability for content/style under partial-label or multi-view weak supervision, with finite-sample gradient-descent convergence for independent subspace models, and a style guidance regularizer.
Problem
Diffusion models generate samples via a stochastic, non-invertible mapping of latent variables, so classical identifiability/ICA arguments do not apply; it is unclear when conditional diffusion models learn identifiably disentangled content and style representations.
Approach
Introduce approximate disentanglement notions ((ε,ν)-disentanglement via mutual information and ε-editability via TV distance) for stochastic non-invertible mixing, prove DM-based disentanglement under partial supervision or multi-view inputs, and for independent subspace models prove finite-sample global convergence of gradient descent with a style guidance regularizer that zeroes out content in
Key results
- On GMM subspace recovery, DM consistently recovers the content subspace (error < 0.1) in four random trials with sufficiently large style guidance weight and sample size.
- On IEMOCAP, the DM-based voice conversion approach achieves higher emotion classification accuracy than no conversion, pitch shifting, and recent VCA baselines, improving as more target speakers are used.
- Theory: DMs achieve (ε,ν)-disentanglement with ε=O(λ_s σ_X² d_X δ) and ν=O(σ_X² δ²) as noise level δ→0 under content disentanglement.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add style guidance regularization with sufficiently large weight | Diffusion model on latent subspace GMMs · Latent subspace GMMs | subspace recovery error | Helped |
| Increase the sample size | Diffusion model on latent subspace GMMs · Latent subspace GMMs | subspace recovery error | Helped |
| Add the proposed regularizer (ablation) | Diffusion model for MNIST colorization · MNIST | disentanglement quality | Helped |
| Add the proposed regularizer (ablation) | Diffusion model for CIFAR-10 denoising · CIFAR-10 | disentanglement quality | Helped |
| Use style guidance weight 3 instead of 0 (ablation) | Diffusion model for MNIST colorization · MNIST | disentanglement quality | Helped |
| Use style guidance weight 3 instead of 0 (ablation) | Diffusion model for CIFAR-10 denoising · CIFAR-10 | disentanglement quality | Helped |
| Use diffusion-model-based disentanglement instead of no conversion, pitch shifting, or other recent voice-conversion adaptation baselines | Speech emotion recognition system · IEMOCAP | classification accuracy | Helped |
| Increase the number of target speakers used during training | Diffusion-model-based voice conversion adaptation · IEMOCAP | classification accuracy | Helped |
Surprising findings
- Disentanglement in mutual information sense does not imply editability; a perfectly (0,0)-disentangled encoding can still fail editability due to sign ambiguity.
Limitations
- Theory relies on mild assumptions (sub-Gaussian data, Lipschitz score) and independence of content and style (approximate independence only extended as perturbation).
- Finite-sample convergence proven only for independent subspace models with infinite-width two-layer ReLU networks.
- Experiments are on controlled, small-scale settings; large-scale experiments left for future work.
Experimental setup
Datasets: MNIST CIFAR-10 IEMOCAP Gaussian mixture models (synthetic)
Benchmarks: MNIST CIFAR-10 IEMOCAP
Metrics: subspace recovery error emotion classification accuracy
Baselines: no conversion pitch shifting recent VCA models
Builds on: denoising diffusion probabilistic models independent component analysis classifier-free guidance score-based generative modeling
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- Synergy Between Sufficient Changes and Sparse Mixing Procedure for Disentangled Representation Learning (ICLR 2025 · similarity 0.88)
- Disentangled Representation Learning via Flow Matching (NeurIPS 2026 · similarity 0.88)
- Unsupervised Region-Based Image Editing of Denoising Diffusion Models (AAAI 2025 · similarity 0.88)
- Graph-based Unsupervised Disentangled Representation Learning via Multimodal Large Language Models (NeurIPS 2024 · similarity 0.87)
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