  In this work we introduce a novel stochastic algorithm dubbed SNIPS, which
draws samples from the posterior distribution of any linear inverse problem,
where the observation is assumed to be contaminated by additive white Gaussian
noise. Our solution incorporates ideas from Langevin dynamics and Newton's
method, and exploits a pre-trained minimum mean squared error (MMSE) Gaussian
denoiser. The proposed approach relies on an intricate derivation of the
posterior score function that includes a singular value decomposition (SVD) of
the degradation operator, in order to obtain a tractable iterative algorithm
for the desired sampling. Due to its stochasticity, the algorithm can produce
multiple high perceptual quality samples for the same noisy observation. We
demonstrate the abilities of the proposed paradigm for image deblurring,
super-resolution, and compressive sensing. We show that the samples produced
are sharp, detailed and consistent with the given measurements, and their
diversity exposes the inherent uncertainty in the inverse problem being solved.
