论文标题
采样与学习分数一样容易：具有最小数据假设的扩散模型的理论
Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions
论文作者
论文摘要
我们为基于分数的生成模型（SGM）提供理论收敛保证，例如deno延伸概率模型（DDPMS），这构成了大型现实世界中生成模型（例如DALL $ \ cdot $ e 2）的骨干。与先前的工作相反，我们的结果（1）以$ l^2 $准确的分数估算（而不是$ l^\ infty $ -CACCRATE）保持； （2）不需要限制性的功能不平等条件，而这些条件排除了实质性的非con虫； （3）在所有相关问题参数中多项式缩放； （4）匹配最新的复杂性保证了兰格文扩散的离散化，前提是得分误差足够小。我们认为这是SGM的经验成功的强有力理论理由。我们还基于严重阻尼的Langevin扩散（CLD）检查了SGM。与传统的观点相反，我们提供了证据，表明CLD的使用不会降低SGM的复杂性。
We provide theoretical convergence guarantees for score-based generative models (SGMs) such as denoising diffusion probabilistic models (DDPMs), which constitute the backbone of large-scale real-world generative models such as DALL$\cdot$E 2. Our main result is that, assuming accurate score estimates, such SGMs can efficiently sample from essentially any realistic data distribution. In contrast to prior works, our results (1) hold for an $L^2$-accurate score estimate (rather than $L^\infty$-accurate); (2) do not require restrictive functional inequality conditions that preclude substantial non-log-concavity; (3) scale polynomially in all relevant problem parameters; and (4) match state-of-the-art complexity guarantees for discretization of the Langevin diffusion, provided that the score error is sufficiently small. We view this as strong theoretical justification for the empirical success of SGMs. We also examine SGMs based on the critically damped Langevin diffusion (CLD). Contrary to conventional wisdom, we provide evidence that the use of the CLD does not reduce the complexity of SGMs.
