作者：Matthew Tivnan Jacopo Teneggi Tzu-Cheng Lee Ruoqiao Zhang Kirsten Boedeker Liang Cai Grace J. Gang Jeremias Sulam J. Webster Stayman
基于分数的随机去噪模型最近被证明是用于条件和无条件图像生成的强大机器学习工具。现有方法基于前向随机过程，其中训练图像随着时间被缩放为零，并且白噪声被逐渐添加，使得最终时间步长近似为零均值同一协方差高斯噪声。然后训练神经网络来近似该时间步长的时间相关得分函数或概率密度对数的梯度。使用该分数估计器，可以运行时间反转随机过程的近似值，以从训练数据分布中采样新图像。这些基于分数的生成模型已经被证明在使用标准基准和度量的情况下优于生成对抗性神经网络。然而，这种方法的一个问题是，它需要神经网络的大量前向传递。附加
Score-based stochastic denoising models have recently been demonstrated as powerful machine learning tools for conditional and unconditional image generation. The existing methods are based on a forward stochastic process wherein the training images are scaled to zero over time and white noise is gradually added such that the final time step is approximately zero-mean identity-covariance Gaussian noise. A neural network is then trained to approximate the time-dependent score function, or the gradient of the logarithm of the probability density, for that time step. Using this score estimator, it is possible to run an approximation of the time-reversed stochastic process to sample new images from the training data distribution. These score-based generative models have been shown to out-perform generative adversarial neural networks using standard benchmarks and metrics. However, one issue with this approach is that it requires a large number of forward passes of the neural network. Additionally, the images at intermediate time steps are not useful, since the signal-to-noise ratio is low. In this work we present a new method called Fourier Diffusion Models which replaces the scalar operations of the forward process with shift-invariant convolutions and the additive white noise with additive stationary noise. This allows for control of MTF and NPS at intermediate time steps. Additionally, the forward process can be crafted to converge to the same MTF and NPS as the measured images. This way, we can model continuous probability flow from true images to measurements. In this way, the sample time can be used to control the tradeoffs between measurement uncertainty and generative uncertainty of posterior estimates. We compare Fourier diffusion models to existing scalar diffusion models and show that they achieve a higher level of performance and allow for a smaller number of time steps.
论文链接：http://arxiv.org/pdf/2303.13285v1
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