3.8 Diffusion Probabilistic Model
Diffusion probabilistic models, inspired by non-equilibrium thermodynamics [186, 508], have
proven to be highly effective for generating high-quality images and audio. These models create a
Markov chain of diffusion steps (𝑥𝑡 ∼ 𝑞(𝑥𝑡|𝑥𝑡−1)) from the original data (𝑥0) to the latent variable
𝑥𝑇 ∼ N(0, I) by gradually adding pre-scheduled noise to the data. The reverse diffusion process
then reconstructs the desired data samples (𝑥0) from the noise 𝑥𝑇 , as shown in Figure 7. Unlike
VAE or flow models, diffusion models keep the dimensionality of the latent variables fixed. While
mostly used for image and audio synthesis, diffusion models have potential applications in speech-
processing tasks, such as speech synthesis and enhancement. This section offers a comprehensive
overview of the fundamental principles of diffusion models and explores their potential uses in the
speech domain.

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