A Practical Diffusion Path for Sampling
This work addresses a specific bottleneck in generative modeling for researchers and practitioners dealing with intractable distributions, though it appears incremental as it builds on existing diffusion and Langevin dynamics frameworks.
The paper tackles the problem of sampling from target distributions where samples are unavailable, by proposing a dilation path method that yields closed-form score vectors, and demonstrates improved performance over classical alternatives in various tasks.
Diffusion models are state-of-the-art methods in generative modeling when samples from a target probability distribution are available, and can be efficiently sampled, using score matching to estimate score vectors guiding a Langevin process. However, in the setting where samples from the target are not available, e.g. when this target's density is known up to a normalization constant, the score estimation task is challenging. Previous approaches rely on Monte Carlo estimators that are either computationally heavy to implement or sample-inefficient. In this work, we propose a computationally attractive alternative, relying on the so-called dilation path, that yields score vectors that are available in closed-form. This path interpolates between a Dirac and the target distribution using a convolution. We propose a simple implementation of Langevin dynamics guided by the dilation path, using adaptive step-sizes. We illustrate the results of our sampling method on a range of tasks, and shows it performs better than classical alternatives.