In this paper, we point out that suboptimal noise-data mapping leads to slow training of diffusion models.

This urges the development of more computation and communication efficient optimization algorithms.

Artificial neural networks are among the most successful modern machine learning methods, in particular because their non-linear parametrization provides a flexible way to implement feature learning (see, e.g., Goodfellow et al., 2016, chapter 15).

Estimating the density of a distribution from samples is a fundamental problem in statistics. In many practical settings, the Wasserstein distance is an appropriate error metric for density estimation. For example, when estimating population densities in a geographic region, a small Wasserstein distance means that the estimate is able to capture roughly where the population mass is. In this work we study differentially private density estimation in the Wasserstein distance. We design and analyze instance-optimal algorithms for this problem that can adapt to easy instances.

In contrast to V AE-based neural compression, where the (mean) decoder is a deterministic neural network, our decoder is a conditional diffusion model. Our approach thus introduces an additional "content" latent variable on which the reverse diffusion process

But, our current design has a limitation: the transition direction and distance are fixed, resulting in equally spaced distances between viewports.