This talk will outline recent NASA AMT-funded advances in the use of generative machine learning models for data assimilation. Specifically, we will leverage the ability of deep learning denoising diffusion models which are able to learn probabilistic mappings to target data conditioned on input context. We develop and apply this paradigm to generating future background ensembles given reanalysis at the current timestep. Next, we will also outline recent results from the numerical analysis of deep learning emulators for chaotic dynamical systems where we probe the conditions under which the emulator of the forward model also recovers the correct tangent-linear adjoint with applications to surrogate accelerated data assimilation.