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Provable Sample-Efficient Transfer Learning Conditional Diffusion Models via Representation Learning

NeurIPS 2025 · Image generation › Fast diffusion sampling · approach: Diffusion theory and design space · 1 citations (OpenAlex)

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Provides the first statistical guarantees for transfer and meta-learning of conditional diffusion models via a shared low-dimensional condition representation, showing sample-complexity gains when the target has few samples.

Problem

Theoretical understanding of why transfer learning conditional diffusion models is sample-efficient, given that a shared low-dimensional representation of conditions is learned from source tasks and only the score network is fine-tuned on scarce target data.

Approach

Assumes a shared low-dimensional condition representation across source and target conditional distributions, proves generalization bounds for transferring score matching error (under task diversity and under a meta-distribution), and derives end-to-end TV distance bounds using deep ReLU approximation, with applications to amortized variational inference and behavior cloning.

Key results

• On the synthetic conditioned diffusion task with beta_0=5.5, fine-tuning gives MSE 14.47 vs 21.99 for train-from-scratch at m=10, and 1.90 vs 1.77 at m=50 (gap narrows as m grows).
• On MNIST image restoration with m=10, fine-tuning MSE is 0.3799 vs 0.4409 for train-from-scratch; fine-tuning is better at every m in {10,...,100}.
• Theory: transfer bound scales as (m/nu wedge n)^{-1/(d_x+d_y+9)} + (nK)^{-1/(D_y+2)} versus m^{-1/(d_x+D_y+9)} for training from scratch.

Measured effects reported in the paper

Surprising findings

• Fine-tuned models are slightly worse than train-from-scratch at m=50 for beta_0=5.5 in the synthetic experiment, attributed to randomness.
• Fine-tuned MSE at beta_0=5.5 with m=50 (1.90) is higher than train-from-scratch (1.77).

Limitations

• Task diversity assumption is hard to verify in practice.
• Analysis covers ERM estimators rather than optimization-based fine-tuning such as LoRA.
• Results apply mainly when the conditional encoder constitutes a substantial part of the model.

Experimental setup

Datasets: MNIST synthetic conditioned diffusion (Langevin SDE)

Benchmarks: synthetic conditioned diffusion MNIST image restoration

Metrics: MSE of posterior mean estimate TV distance bound (theoretical)

Baselines: train-from-scratch

Builds on: denoising score matching task diversity transfer learning theory meta-learning theory with environment assumption diffusion model score approximation theory

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