Closed-Form Diffusion Models
This work addresses the computational and generalization challenges in generative modeling for researchers and practitioners, though it is incremental as it builds on existing SGM frameworks.
The authors tackled the problem of score-based generative models (SGMs) memorizing training data and being costly to train and sample by explicitly smoothing the closed-form score to generate novel samples without training, achieving competitive sampling times on consumer-grade CPUs.
Score-based generative models (SGMs) sample from a target distribution by iteratively transforming noise using the score function of the perturbed target. For any finite training set, this score function can be evaluated in closed form, but the resulting SGM memorizes its training data and does not generate novel samples. In practice, one approximates the score by training a neural network via score-matching. The error in this approximation promotes generalization, but neural SGMs are costly to train and sample, and the effective regularization this error provides is not well-understood theoretically. In this work, we instead explicitly smooth the closed-form score to obtain an SGM that generates novel samples without training. We analyze our model and propose an efficient nearest-neighbor-based estimator of its score function. Using this estimator, our method achieves competitive sampling times while running on consumer-grade CPUs.