  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.
