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We propose denoising diffusion variational inference (DDVI), an approximate
inference algorithm for latent variable models which relies on diffusion models
as expressive variational posteriors. Our method augments variational
posteriors with auxiliary latents, which yields an expressive class of models
that perform diffusion in latent space by reversing a user-specified noising
process. We fit these models by optimizing a novel lower bound on the marginal
likelihood inspired by the wake-sleep algorithm. Our method is easy to
implement (it fits a regularized extension of the ELBO), is compatible with
black-box variational inference, and outperforms alternative classes of
approximate posteriors based on normalizing flows or adversarial networks. When
applied to deep latent variable models, our method yields the denoising
diffusion VAE (DD-VAE) algorithm. We use this algorithm on a motivating task in
biology -- inferring latent ancestry from human genomes -- outperforming strong
baselines on the Thousand Genomes dataset.