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Diffusion probabilistic models (DPMs) and their extensions have emerged ascompetitive generative models yet confront challenges of efficient sampling. Wepropose a new bilateral denoising diffusion model (BDDM) that parameterizesboth the forward and reverse processes with a schedule network and a scorenetwork, which can train with a novel bilateral modeling objective. We showthat the new surrogate objective can achieve a lower bound of the log marginallikelihood tighter than a conventional surrogate. We also find that BDDM allowsinheriting pre-trained score network parameters from any DPMs and consequentlyenables speedy and stable learning of the schedule network and optimization ofa noise schedule for sampling. Our experiments demonstrate that BDDMs cangenerate high-fidelity audio samples with as few as three sampling steps.Moreover, compared to other state-of-the-art diffusion-based neural vocoders,BDDMs produce comparable or higher quality samples indistinguishable from humanspeech, notably with only seven sampling steps (143x faster than WaveGrad and28.6x faster than DiffWave). We release our code athttps://github.com/tencent-ailab/bddm.

BDDM: Bilateral Denoising Diffusion Models for Fast and High-Quality Speech Synthesis