Variational objectives for amortized Bayesian inference in inverse problems: The role of posterior conditioning

arXiv:2609.25145 · stat.ML, cs.CE, cs.IT, cs.LG, cs.NA, math.IT, math.NA · Submitted 2026-09-21 · Read on arXiv

stat.ML, cs.CE, cs.IT, cs.LG, cs.NA, math.IT, math.NA

Submitted: 2026-09-21

Updated: 2026-09-21

Comments: 50 pages

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Inverse Problem — 92× in this paper · explained in 2 episodes
• Benchmark — 40× in this paper · explained in 2 episodes
• Regularization — 40× in this paper · explained in 3 episodes
• Accuracy — 32× in this paper · explained in 1 episode
• Wasserstein Distance — 31× in this paper · explained in 4 episodes
• 2-Wasserstein Distance — 17× in this paper · explained in 1 episode
• Fisher Information — 14× in this paper · explained in 3 episodes
• Loss Function — 13× in this paper · explained in 2 episodes
• Bayesian Inference — 10× in this paper · explained in 5 episodes
• Adaptive Metropolis — 7× in this paper
• Anisotropy — 5× in this paper · explained in 3 episodes
• KL Regularization — 5× in this paper · explained in 2 episodes
• Uncertainty Quantification — 5× in this paper · explained in 8 episodes
• Adam — 4× in this paper · explained in 2 episodes
• Generative Model — 4× in this paper · explained in 2 episodes
• Latent Space — 4× in this paper · explained in 7 episodes
• Flow Matching — 3× in this paper · explained in 8 episodes
• Generative Models — 3× in this paper · explained in 2 episodes
• Reconstruction Error — 3× in this paper · explained in 2 episodes
• Simulation-based Inference — 3× in this paper · explained in 2 episodes
• Adaptation — 2× in this paper · explained in 1 episode
• Consistency — 2× in this paper · explained in 3 episodes
• Data Assimilation — 2× in this paper · explained in 2 episodes
• DeepONet — 2× in this paper · explained in 2 episodes
• Generative Modeling — 2× in this paper · explained in 3 episodes
• Markov Chain Monte Carlo — 2× in this paper
• Normalizing Flow — 2× in this paper · explained in 3 episodes
• Normalizing Flows — 2× in this paper · explained in 4 episodes
• Two-stage training — 2× in this paper · explained in 2 episodes
• Variational Autoencoder (VAE) — 2× in this paper · explained in 3 episodes
• Variational Bayes — 2× in this paper · explained in 2 episodes
• Adjoint Method — 1× in this paper · explained in 1 episode
• Calibration — 1× in this paper · explained in 7 episodes
• Delayed Rejection Adaptive Metropolis — 1× in this paper
• Diffusion Model — 1× in this paper · explained in 8 episodes
• Diffusion Models — 1× in this paper · explained in 6 episodes
• Error Decomposition — 1× in this paper · explained in 3 episodes
• Optimal Transport — 1× in this paper · explained in 5 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Deep Bayesian Inversion
• Auto-Encoding Variational Bayes

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