KL Convergence Guarantees for Score diffusion models under minimal data assumptions

Understand

Diffusion models are a new class of generative models that revolve around the estimation of the score function associated with a stochastic differential equation.

• Subsequent to its acquisition, the approximated score function is then harnessed to simulate the corresponding time-reversal process, ultimately enabling the generation of approximate data samples.
• Despite their evident practical significance these models carry, a notable challenge persists in the form of a lack of comprehensive quantitative results, especially in scenarios involving non-regular scores and estimators.
• In almost all reported bounds in Kullback Leibler (KL) divergence, it is assumed that either the score function or its approximation is Lipschitz uniformly in time.