Denoising Diffusion Probabilistic Models have shown extraordinary ability on various generative tasks. However, their slow inference speed renders them impractical in speech synthesis. This paper proposes a linear diffusion model (LinDiff) based on an ordinary differential equation to simultaneously reach fast inference and high sample quality. Firstly, we employ linear interpolation between the target and noise to design a diffusion sequence for training, while previously the diffusion path that links the noise and target is a curved segment. When decreasing the number of sampling steps (i.e., the number of line segments used to fit the path), the ease of fitting straight lines compared to curves allows us to generate higher quality samples from a random noise with fewer iterations. Secondly, to reduce computational complexity and achieve effective global modeling of noisy speech, LinDiff employs a patch-based processing approach that partitions the input signal into small patches. The patch-wise token leverages Transformer architecture for effective modeling of global information. Adversarial training is used to further improve the sample quality with decreased sampling steps. We test proposed method with speech synthesis conditioned on acoustic feature (Mel-spectrograms). Experimental results verify that our model can synthesize high-quality speech even with only one diffusion step. Both subjective and objective evaluations demonstrate that our model can synthesize speech of a quality comparable to that of autoregressive models with faster synthesis speed (3 diffusion steps).

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