  Denoising diffusion probabilistic models (diffusion models for short) require
a large number of iterations in inference to achieve the generation quality
that matches or surpasses the state-of-the-art generative models, which
invariably results in slow inference speed. Previous approaches aim to optimize
the choice of inference schedule over a few iterations to speed up inference.
However, this results in reduced generation quality, mainly because the
inference process is optimized separately, without jointly optimizing with the
training process. In this paper, we propose InferGrad, a diffusion model for
vocoder that incorporates inference process into training, to reduce the
inference iterations while maintaining high generation quality. More
specifically, during training, we generate data from random noise through a
reverse process under inference schedules with a few iterations, and impose a
loss to minimize the gap between the generated and ground-truth data samples.
Then, unlike existing approaches, the training of InferGrad considers the
inference process. The advantages of InferGrad are demonstrated through
experiments on the LJSpeech dataset showing that InferGrad achieves better
voice quality than the baseline WaveGrad under same conditions while
maintaining the same voice quality as the baseline but with $3$x speedup ($2$
iterations for InferGrad vs $6$ iterations for WaveGrad).
