?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=Posterior+Sampling+Based+on+Gradient+Flows+of+the+MMD+with+Negative+Distance+Kernel&rft.creator=Hagemann%2C+Paul&rft.creator=Hertrich%2C+Johannes&rft.creator=Altekr%C3%BCger%2C+Fabian&rft.creator=Beinert%2C+Robert&rft.creator=Chemseddine%2C+Jannis&rft.creator=Steidl%2C+Gabriele&rft.description=We+propose+conditional+flows+of+the+maximum+mean+discrepancy+(MMD)+with+the+negative+distance+kernel+for+posterior+sampling+and+conditional+generative+modelling.+This+MMD%2C+which+is+also+known+as+energy+distance%2C+has+several+advantageous+properties+like+efficient+computation+via+slicing+and+sorting.+We+approximate+the+joint+distribution+of+the+ground+truth+and+the+observations+using+discrete+Wasserstein+gradient+flows+and+establish+an+error+bound+for+the+posterior+distributions.+Further%2C+we+prove+that+our+particle+flow+is+indeed+a+Wasserstein+gradient+flow+of+an+appropriate+functional.+The+power+of+our+method+is+demonstrated+by+numerical+examples+including+conditional+image+generation+and+inverse+problems+like+superresolution%2C+inpainting+and+computed+tomography+in+low-dose+and+limited-angle+settings.&rft.subject=Bayesian+inverse+Problems%2C+MMD%2C+Gradient+Flows%2C+Deep+Learning&rft.publisher=ICLR&rft.date=2024-04-08&rft.type=Proceedings+paper&rft.language=eng&rft.source=+++++In%3A++Proceedings+of+the+Twelfth+International+Conference+on+Learning+Representations+%3A+ICLR+2024.++++ICLR%3A+Vienna%2C+Austria.+(2024)+++++&rft.format=application%2Fpdf&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F10194632%2F1%2Fposterior.pdf&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F10194632%2F&rft.rights=open