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Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data
Minshuo Chen · Kaixuan Huang · Tuo Zhao · Mengdi Wang

Thu Jul 27 04:30 PM -- 06:00 PM (PDT) @ Exhibit Hall 1 #530

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. Our result provides sample complexity bounds for distribution estimation using diffusion models. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. Further, the generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution. The convergence rate depends on subspace dimension, implying that diffusion models can circumvent the curse of data ambient dimensionality.

Author Information

Minshuo Chen (Princeton University)
Kaixuan Huang (Princeton University)
Tuo Zhao (Georgia Tech)
Mengdi Wang (Princeton University)

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