Beyond Scores: Proximal Diffusion Models.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Computational Statistics

Background:

• Diffusion models are powerful generative tools for high-dimensional data.
• Their effectiveness relies on score estimation via denoisers and forward stochastic differential equation (SDE) discretization.

Purpose of the Study:

• To introduce Proximal Diffusion Models (ProxDM) using backward SDE discretization.
• To demonstrate theoretical and practical advantages over traditional score-matching techniques.

Main Methods:

• Leveraging proximal matching to learn proximal operators of the log-density.
• Implementing backward discretization of SDEs with proximal maps instead of scores.
• Developing Proximal Diffusion Models (ProxDM).

Main Results:

• Theoretical proof that O(d/√ε) steps suffice for ε-accurate KL divergence distribution generation.
• Empirical demonstration of significantly faster convergence in ProxDM variants.
• Achieved rapid generation with only a few sampling steps.

Conclusions:

• Proximal Diffusion Models offer a theoretically sound and empirically efficient alternative to score-matching diffusion models.
• ProxDM enables faster generative sampling, particularly beneficial for high-dimensional data.
• The use of proximal maps in backward SDE discretization unlocks new avenues for generative modeling.