  Diffusion probabilistic models (DPMs) and their extensions have emerged as
competitive generative models yet confront challenges of efficient sampling. We
propose a new bilateral denoising diffusion model (BDDM) that parameterizes
both the forward and reverse processes with a schedule network and a score
network, which can train with a novel bilateral modeling objective. We show
that the new surrogate objective can achieve a lower bound of the log marginal
likelihood tighter than a conventional surrogate. We also find that BDDM allows
inheriting pre-trained score network parameters from any DPMs and consequently
enables speedy and stable learning of the schedule network and optimization of
a noise schedule for sampling. Our experiments demonstrate that BDDMs can
generate 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 human
speech, notably with only seven sampling steps (143x faster than WaveGrad and
28.6x faster than DiffWave). We release our code at
https://github.com/tencent-ailab/bddm.
