Diffusion models have been successful on a range of conditional generation
tasks including molecular design and text-to-image generation. However, these
achievements have primarily depended on task-specific conditional training or
error-prone heuristic approximations. Ideally, a conditional generation method
should provide exact samples for a broad range of conditional distributions
without requiring task-specific training. To this end, we introduce the Twisted
Diffusion Sampler, or TDS. TDS is a sequential Monte Carlo (SMC) algorithm that
targets the conditional distributions of diffusion models. The main idea is to
use twisting, an SMC technique that enjoys good computational efficiency, to
incorporate heuristic approximations without compromising asymptotic exactness.
We first find in simulation and on MNIST image inpainting and class-conditional
generation tasks that TDS provides a computational statistical trade-off,
yielding more accurate approximations with many particles but with empirical
improvements over heuristics with as few as two particles. We then turn to
motif-scaffolding, a core task in protein design, using a TDS extension to
Riemannian diffusion models. On benchmark test cases, TDS allows flexible
conditioning criteria and often outperforms the state of the art.

本文提出了一种名为 Twisted Diffusion Sampler 的串行蒙特卡罗算法用于生成条件分布，该算法具有更高的计算效率和更准确的近似度，并成功应用于蛋白质设计。

扩散模型中实用且渐近精确的条件抽样

Practical and Asymptotically Exact Conditional Sampling in Diffusion  Models

The traditional way of tackling discrete optimization problems is by using
local search on suitably defined cost or fitness landscapes. Such approaches
are however limited by the slowing down that occurs when local minima, that are
a feature of the typically rugged landscapes encountered, arrest the progress
of the search process. Another way of tackling optimization problems is by the
use of heuristic approximations to estimate a global cost minimum. Here we
present a combination of these two approaches by using cover-encoding maps
which map processes from a larger search space to subsets of the original
search space. The key idea is to construct cover-encoding maps with the help of
suitable heuristics that single out near-optimal solutions and result in
landscapes on the larger search space that no longer exhibit trapping local
minima. The processes that are typically employed involve some form of
coarse-graining, and we suggest here that they can be viewed as avatars of
renormalisation group transformations.

文章介绍了利用局部搜索和启发式逼近相结合的方法来解决离散优化问题，通过构建适当的启发式覆盖映射，实现从较大的搜索空间映射到原始搜索空间的子集，来避免困局性局部最小值的出现，并指出这种方法实际上可以被看做是重正化群变换的一种应用。