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To resolve sampling biases in decoder-free diffusion inverse problem solvers, this work introduces ANaLOG, a framework that weights native-latent guidance using an input- and timestep-dependent anisotropic covariance. The authors prove in a linear setting that anisotropic, uncertainty-aware weighting is theoretically necessary for exact posterior sampling, whereas conventional isotropic guidance guarantees sampling error. Evaluated across five inverse problems, ANaLOG consistently outperforms prior surrogate guidance techniques in perceptual reconstruction quality without sacrificing latent-space inference speed.
Standard latent diffusion guidance provably samples from the wrong posterior by assuming isotropic uncertainty across latent dimensions—an error resolved by learning time- and input-dependent directional covariances.
Native-latent guidance is a recent paradigm for solving inverse problems with latent diffusion models. It replaces repeated evaluations of the image-space forward model, each requiring a decoder pass, with efficient guidance computed using a learned latent-space surrogate. However, existing methods apply guidance uniformly across latent dimensions, ignoring that measurements are informative only along certain directions and that the reliability of model predictions varies across inputs and timesteps. We propose ANaLOG, a framework for efficient uncertainty-aware guidance with pretrained latent diffusion models. ANaLOG models uncertainty by learning an anisotropic, input- and time-dependent covariance that is integrated into the guidance mechanism to emphasize reliable directions and downweight uncertain ones. We theoretically analyze this framework in a linear model setting and prove that anisotropic, uncertainty-aware weighting is necessary for correct sampling, whereas isotropic guidance induces sampling errors. Experiments across five challenging inverse problems show that ANaLOG improves perceptual reconstruction quality over existing methods while preserving efficiency.