We propose a framework to perform Bayesian inference using conditional
score-based diffusion models to solve a class of inverse problems in mechanics
involving the inference of a specimen's spatially varying material properties
from noisy measurements of its mechanical response to loading. Conditional
score-based diffusion models are generative models that learn to approximate
the score function of a conditional distribution using samples from the joint
distribution. More specifically, the score functions corresponding to multiple
realizations of the measurement are approximated using a single neural network,
the so-called score network, which is subsequently used to sample the posterior
distribution using an appropriate Markov chain Monte Carlo scheme based on
Langevin dynamics. Training the score network only requires simulating the
forward model. Hence, the proposed approach can accommodate black-box forward
models and complex measurement noise. Moreover, once the score network has been
trained, it can be re-used to solve the inverse problem for different
realizations of the measurements. We demonstrate the efficacy of the proposed
approach on a suite of high-dimensional inverse problems in mechanics that
involve inferring heterogeneous material properties from noisy measurements.
Some examples we consider involve synthetic data, while others include data
collected from actual elastography experiments. Further, our applications
demonstrate that the proposed approach can handle different measurement
modalities, complex patterns in the inferred quantities, non-Gaussian and
non-additive noise models, and nonlinear black-box forward models. The results
show that the proposed framework can solve large-scale physics-based inverse
problems efficiently.

我们提出了一个框架，使用条件分数扩散模型执行贝叶斯推理来解决机械学中涉及由加载的噪声测量推断出具有空间变化的材料属性的一类反问题。

机械领域中解决反问题的条件评分扩散模型

Conditional score-based diffusion models for solving inverse problems in  mechanics

Recently, conditional score-based diffusion models have gained significant
attention in the field of supervised speech enhancement, yielding
state-of-the-art performance. However, these methods may face challenges when
generalising to unseen conditions. To address this issue, we introduce an
alternative approach that operates in an unsupervised manner, leveraging the
generative power of diffusion models. Specifically, in a training phase, a
clean speech prior distribution is learnt in the short-time Fourier transform
(STFT) domain using score-based diffusion models, allowing it to
unconditionally generate clean speech from Gaussian noise. Then, we develop a
posterior sampling methodology for speech enhancement by combining the learnt
clean speech prior with a noise model for speech signal inference. The noise
parameters are simultaneously learnt along with clean speech estimation through
an iterative expectationmaximisation (EM) approach. To the best of our
knowledge, this is the first work exploring diffusion-based generative models
for unsupervised speech enhancement, demonstrating promising results compared
to a recent variational auto-encoder (VAE)-based unsupervised approach and a
state-of-the-art diffusion-based supervised method. It thus opens a new
direction for future research in unsupervised speech enhancement.

最近，条件评分驱动扩散模型在监督式语音增强领域引起了显著关注，取得了最先进的性能。然而，这些方法在泛化到未见条件时可能面临挑战。为了解决这个问题，我们引入了一种在无监督方式下操作、利用扩散模型的生成能力的替代方法。具体而言，训练阶段，在短时傅里叶变换（STFT）领域中使用评分驱动扩散模型学习了干净语音的先验分布，使其能够从高斯噪声中无条件地生成干净语音。然后，我们开发了一种通过将学习的干净语音先验与噪声模型结合起来进行语音增强的后验采样方法。噪声参数通过迭代的期望最大化（EM）方法与干净语音估计同时学习。据我们所知，这是第一个探索基于扩散的生成模型用于无监督语音增强的工作，与最近的变分自编码器（VAE）无监督方法和最先进的基于扩散的监督方法相比，取得了有希望的结果。因此，它为未来的无监督语音增强研究开辟了新的方向。