Probabilistic seismic interpolation with the implicit Prior of a Deep Denoiser

Geophysicists have long recognized the importance of quantifying the uncertainty associated with geophysical inverse problems, whether they are used for processing, imaging, or parameter estimation purposes. The inability to create representative prior and proposal distributions has, however, hindered the widespread adoption of acceptance-rejection algorithms, such as those from the family of Monte-Carlo Markov Chain methods. We present a flexible approach to probabilistic sampling that leverages the ability of denoising neural networks to provide direct access to the gradient of the log-probability of interest. The proposed algorithm can produce high-quality, diverse samples from both unconditional and conditional probability distributions, the latter being of particular interest when solving probabilistic inverse problems. A successful application is presented in the context of seismic interpolation on both synthetic and field data.