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In this paper, we propose a general framework for nonlinear multigrid inversion applicable to any inverse problem in which the forward model can be naturally represented at differing resolutions. In multigrid inversion, the problem is adjusted at each resolution by using the solutions at both finer and coarser resolutions. To do this, we formulate a consistent set of cost functional across resolutions. At each resolution, both the forward and inverse problems are discretized at the lower resolution; thus reducing computation. Simulation results for the problem of optical diffusion tomography indicate that multigrid inversion can dramatically reduce computation in this application.