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arXiv

SIMCA calibrates guidance weights offline by least squares, letting diffusion and flow-matching posterior sampling match or beat prior methods within 50 steps

The authors introduce SIMCA: observing that the conditional denoising score-matching objective for diffusion models and the conditional flow-matching objective for flow-matching models are least-squares objectives in the guidance weights at each time step, they reduce guidance-weight tuning in training-free posterior sampling to a two-dimensional linear least-squares problem solved offline by a greedy simulation-based calibration that needs only a single minibatch of sampling trajectories and no retraining; across several inverse problems on FFHQ, ImageNet, CelebA and AFHQ-Cat, the method matches or surpasses state-of-the-art training-free methods and lets diffusion samplers cut steps from 1000 to 50 without significant degradation in reconstruction quality.