psnr
Tempered Guided Diffusion
Makris, Andreas, Fearnhead, Paul, Nemeth, Chris
Training-free conditional diffusion provides a flexible alternative to task-specific conditional model training, but existing samplers often allocate computation inefficiently: independent guided trajectories can vary widely in quality, and additional function evaluations along a single trajectory may not recover from poor early decisions. We propose Tempered Guided Diffusion (TGD), an annealed sequential Monte Carlo framework for training-free conditional sampling with diffusion priors. TGD targets tempered posterior distributions over the clean signal, using noisy diffusion states only as auxiliary variables for proposing reconstructions and propagating particles. Particles are reweighted by incremental likelihood ratios, resampled, and propagated across noise levels, concentrating computation on trajectories plausible under both the prior and observation. Under idealized exact-reconstruction assumptions, full TGD yields a consistent particle approximation to the posterior as the number of particles grows. For expensive reconstruction tasks, Accelerated TGD (A-TGD) retains early particle exploration but prunes to a single high-likelihood trajectory partway through sampling. Experiments on a controlled two-dimensional inverse problem and image inverse problems show improved posterior approximation and favorable wall-clock speed-quality tradeoffs over independent multi-trajectory baselines.
Appendix AUse of Image Prediction
In addition to our main results presented in Section 4 of the paper, we also performed various exploratory experiments to investigate further application cases of the METASIN activations. The experiments cover image classification where we show favorable results of using convolutional METASIN networks over baseline RELU networks, as well as various overfitting experiments to explore the use of METASIN activations with MLPs. In all MLP experiments, we use METASIN with K = 10 sine components, and distribute the frequencies evenly across the range [1,35]. The initialization of the remaining parameters follows the description provided in Section 3. Bicycle Figure 5: Visualization of selected reconstructed frames of the video. To fully appreciate the details and visual cues presented in the figure, we recommend visualizing the figures in color and zooming in for a more comprehensive analysis.