Diffusion models in the literature are optimized with various objectives that
are special cases of a weighted loss, where the weighting function specifies
the weight per noise level. Uniform weighting corresponds to maximizing the
ELBO, a principled approximation of maximum likelihood. In current practice
diffusion models are optimized with non-uniform weighting due to better results
in terms of sample quality. In this work we expose a direct relationship
between the weighted loss (with any weighting) and the ELBO objective.
We show that the weighted loss can be written as a weighted integral of
ELBOs, with one ELBO per noise level. If the weighting function is monotonic,
then the weighted loss is a likelihood-based objective: it maximizes the ELBO
under simple data augmentation, namely Gaussian noise perturbation. Our main
contribution is a deeper theoretical understanding of the diffusion objective,
but we also performed some experiments comparing monotonic with non-monotonic
weightings, finding that monotonic weighting performs competitively with the
best published results.

研究了扩散模型中优化目标的加权损失函数，证明了加权损失函数与最大似然的 ELBO 目标有直接关系，其中加权损失函数是基于似然的目标，如果加权函数是单调的。

将扩散目标理解为 ELBO 的加权积分

Understanding the Diffusion Objective as a Weighted Integral of ELBOs

Beam search is a popular satisficing approach to heuristic search problems
that allows one to trade increased computation time for lower solution cost by
increasing the beam width parameter. We make two contributions to the study of
beam search. First, we show how to make beam search monotonic; that is, we
provide a new variant that guarantees non-increasing solution cost as the beam
width is increased. This makes setting the beam parameter much easier. Second,
we show how using distance-to-go estimates can allow beam search to find better
solutions more quickly in domains with non-uniform costs. Together, these
results improve the practical effectiveness of beam search.

本文提出了通过引入 monotonic beam search 算法和距离估计来提高 beam search 算法的实际效率。