To sample from a general target distribution $p_*\propto e^{-f_*}$ beyond the
isoperimetric condition, Huang et al. (2023) proposed to perform sampling
through reverse diffusion, giving rise to Diffusion-based Monte Carlo (DMC).
Specifically, DMC follows the reverse SDE of a diffusion process that
transforms the target distribution to the standard Gaussian, utilizing a
non-parametric score estimation. However, the original DMC algorithm
encountered high gradient complexity, resulting in an exponential dependency on
the error tolerance $\epsilon$ of the obtained samples. In this paper, we
demonstrate that the high complexity of DMC originates from its redundant
design of score estimation, and proposed a more efficient algorithm, called
RS-DMC, based on a novel recursive score estimation method. In particular, we
first divide the entire diffusion process into multiple segments and then
formulate the score estimation step (at any time step) as a series of
interconnected mean estimation and sampling subproblems accordingly, which are
correlated in a recursive manner. Importantly, we show that with a proper
design of the segment decomposition, all sampling subproblems will only need to
tackle a strongly log-concave distribution, which can be very efficient to
solve using the Langevin-based samplers with a provably rapid convergence rate.
As a result, we prove that the gradient complexity of RS-DMC only has a
quasi-polynomial dependency on $\epsilon$, which significantly improves
exponential gradient complexity in Huang et al. (2023). Furthermore, under
commonly used dissipative conditions, our algorithm is provably much faster
than the popular Langevin-based algorithms. Our algorithm design and
theoretical framework illuminate a novel direction for addressing sampling
problems, which could be of broader applicability in the community.

通过逆扩散过程进行采样的 RS-DMC 算法，利用新颖的递归评分估计方法，设计高效的算法来解决 Diffusion-based Monte Carlo 中高梯度复杂度问题，并在常用耗散条件下证明其比常用 Langevin-based 算法速度更快，为解决采样问题提供了新的方向。

基于扩散的蒙特卡洛方法实现更快的采样

Faster Sampling without Isoperimetry via Diffusion-based Monte Carlo

Estimating the 6D object pose from a single RGB image often involves noise
and indeterminacy due to challenges such as occlusions and cluttered
backgrounds. Meanwhile, diffusion models have shown appealing performance in
generating high-quality images from random noise with high indeterminacy
through step-by-step denoising. Inspired by their denoising capability, we
propose a novel diffusion-based framework (6D-Diff) to handle the noise and
indeterminacy in object pose estimation for better performance. In our
framework, to establish accurate 2D-3D correspondence, we formulate 2D
keypoints detection as a reverse diffusion (denoising) process. To facilitate
such a denoising process, we design a Mixture-of-Cauchy-based forward diffusion
process and condition the reverse process on the object features. Extensive
experiments on the LM-O and YCB-V datasets demonstrate the effectiveness of our
framework.

基于扩散模型和逆扩散算法的 6D 物体姿态估计框架，在减少噪声和不确定性的基础上实现准确的 2D-3D 对应，并通过对物体特征进行条件优化，取得了较好的性能。

6D-Diff: 一个用于 6D 物体姿态估计的关键点扩散框架

6D-Diff: A Keypoint Diffusion Framework for 6D Object Pose Estimation

Incorporating physics in human motion capture to avoid artifacts like
floating, foot sliding, and ground penetration is a promising direction.
Existing solutions always adopt kinematic results as reference motions, and the
physics is treated as a post-processing module. However, due to the depth
ambiguity, monocular motion capture inevitably suffers from noises, and the
noisy reference often leads to failure for physics-based tracking. To address
the obstacles, our key-idea is to employ physics as denoising guidance in the
reverse diffusion process to reconstruct physically plausible human motion from
a modeled pose probability distribution. Specifically, we first train a latent
gaussian model that encodes the uncertainty of 2D-to-3D lifting to facilitate
reverse diffusion. Then, a physics module is constructed to track the motion
sampled from the distribution. The discrepancies between the tracked motion and
image observation are used to provide explicit guidance for the reverse
diffusion model to refine the motion. With several iterations, the
physics-based tracking and kinematic denoising promote each other to generate a
physically plausible human motion. Experimental results show that our method
outperforms previous physics-based methods in both joint accuracy and success
rate. More information can be found at
https://github.com/Me-Ditto/Physics-Guided-Mocap.

将物理学应用于人体动作捕捉以避免浮动、脚滑与地面穿透等问题，并利用物理学作为去噪引导来从建模的姿态概率分布中重构合理的人体动作，实验证明我们的方法在关节准确性和成功率上优于之前的基于物理的方法。

基于物理引导的姿态概率建模的人体动作捕捉

Physics-Guided Human Motion Capture with Pose Probability Modeling

Diffusion Models (DMs) have demonstrated state-of-the-art performance in
content generation without requiring adversarial training. These models are
trained using a two-step process. First, a forward - diffusion - process
gradually adds noise to a datum (usually an image). Then, a backward - reverse
diffusion - process gradually removes the noise to turn it into a sample of the
target distribution being modelled. DMs are inspired by non-equilibrium
thermodynamics and have inherent high computational complexity. Due to the
frequent function evaluations and gradient calculations in high-dimensional
spaces, these models incur considerable computational overhead during both
training and inference stages. This can not only preclude the democratization
of diffusion-based modelling, but also hinder the adaption of diffusion models
in real-life applications. Not to mention, the efficiency of computational
models is fast becoming a significant concern due to excessive energy
consumption and environmental scares. These factors have led to multiple
contributions in the literature that focus on devising computationally
efficient DMs. In this review, we present the most recent advances in diffusion
models for vision, specifically focusing on the important design aspects that
affect the computational efficiency of DMs. In particular, we emphasize the
recently proposed design choices that have led to more efficient DMs. Unlike
the other recent reviews, which discuss diffusion models from a broad
perspective, this survey is aimed at pushing this research direction forward by
highlighting the design strategies in the literature that are resulting in
practicable models for the broader research community. We also provide a future
outlook of diffusion models in vision from their computational efficiency
viewpoint.

本综述主要介绍了最近视觉领域中扩散模型的进展，特别是那些影响扩散模型计算效率的重要设计方面，重点是强调了最近提出的设计选择，这些选择导致更高效的扩散模型。