Audio Decoding by Inverse Problem Solving

We consider audio decoding as an inverse problem and solve it through diffusion posterior sampling. Explicit conditioning functions are developed for input signal measurements provided by an example of a transform domain perceptual audio codec. Viability is demonstrated by evaluating arbitrary pairings of a set of bitrates and task-agnostic prior models. For instance, we observe significant improvements on piano while maintaining speech performance when a speech model is replaced by a joint model trained on both speech and piano. With a more general music model, improved decoding compared to legacy methods is obtained for a broad range of content types and bitrates. The noisy mean model, underlying the proposed derivation of conditioning, enables a significant reduction of gradient evaluations for diffusion posterior sampling, compared to methods based on Tweedie's mean. Combining Tweedie's mean with our conditioning functions improves the objective performance. An audio demo is available at https://dpscodec-demo.github.io/.