Authors:  Fu Wang, Xinquan Huang, and Tariq Alkhalifah

• We propose a new paradigm, combining diffusion models and FWI, makes use of a prior distribution of our expectations of the subsurface.
• It includes two steps: pretraining diffusion model using random velocity models guided by well information, and implementing FWI regularized by diffusion models.
• The beauty of the diffusion model is that we can store the main features of velocity distribution into the NN, while keeping the model size intact (no latent space), and thus, we are able to generate a velocity model belonging to the distribution via the reverse diffusion process.
• Synthetic and field experiments demonstrate that our method can outperform the conventional FWI with only a small additional computational cost.
• Further, we extend our method to 3D FWI using 2D diffusion model.

Figure 1. The top represents the training workflow of diffusion model; the bottom represents the workflow of diffusion FWI.	Figure 2. Top to bottom: the initial model, the inverted result using conventional FWI, the inverted result using diffusion FWI by OpenFWI model and random model.