Score-based models generate samples by mapping noise to data (and vice versa)
via a high-dimensional diffusion process. We question whether it is necessary
to run this entire process at high dimensionality and incur all the
inconveniences thereof. Instead, we restrict the diffusion via projections onto
subspaces as the data distribution evolves toward noise. When applied to
state-of-the-art models, our framework simultaneously improves sample quality
-- reaching an FID of 2.17 on unconditional CIFAR-10 -- and reduces the
computational cost of inference for the same number of denoising steps. Our
framework is fully compatible with continuous-time diffusion and retains its
flexible capabilities, including exact log-likelihoods and controllable
generation. Code is available at
this https URL

通过在噪声映射运行限制后的高维扩散过程，实现基于评分模型生成高质量样本且减少计算量的方法。

子空间扩散生成模型

Subspace Diffusion Generative Models

Approximate Markov chain Monte Carlo (MCMC) offers the promise of more rapid
sampling at the cost of more biased inference. Since standard MCMC diagnostics
fail to detect these biases, researchers have developed computable Stein
discrepancy measures that provably determine the convergence of a sample to its
target distribution. This approach was recently combined with the theory of
reproducing kernels to define a closed-form kernel Stein discrepancy (KSD)
computable by summing kernel evaluations across pairs of sample points. We
develop a theory of weak convergence for KSDs based on Stein's method,
demonstrate that commonly used KSDs fail to detect non-convergence even for
Gaussian targets, and show that kernels with slowly decaying tails provably
determine convergence for a large class of target distributions. The resulting
convergence-determining KSDs are suitable for comparing biased, exact, and
deterministic sample sequences and simpler to compute and parallelize than
alternative Stein discrepancies. We use our tools to compare biased samplers,
select sampler hyperparameters, and improve upon existing KSD approaches to
one-sample hypothesis testing and sample quality improvement.

本研究基于 Reproducing Kernel 和 Stein method 提出了一种新型的无偏采样方法，通过比较概率分布的差异来衡量采样结果的表现，并在一些目标分布中证明其收敛性和优越性。