  Generative Models (GMs) have attracted considerable attention due to their
tremendous success in various domains, such as computer vision where they are
capable to generate impressive realistic-looking images. Likelihood-based GMs
are attractive due to the possibility to generate new data by a single model
evaluation. However, they typically achieve lower sample quality compared to
state-of-the-art score-based diffusion models (DMs). This paper provides a
significant step in the direction of addressing this limitation. The idea is to
borrow one of the strengths of score-based DMs, which is the ability to perform
accurate density estimation in low-density regions and to address manifold
overfitting by means of data mollification. We connect data mollification
through the addition of Gaussian noise to Gaussian homotopy, which is a
well-known technique to improve optimization. Data mollification can be
implemented by adding one line of code in the optimization loop, and we
demonstrate that this provides a boost in generation quality of
likelihood-based GMs, without computational overheads. We report results on
image data sets with popular likelihood-based GMs, including variants of
variational autoencoders and normalizing flows, showing large improvements in
FID score.
