MCMC-Correction of Score-Based Diffusion Models for Model Composition

• URL: http://arxiv.org/abs/2307.14012v2
• Date: Wed, 10 Jul 2024 09:24:07 GMT
• Title: MCMC-Correction of Score-Based Diffusion Models for Model Composition
• Authors: Anders Sjöberg, Jakob Lindqvist, Magnus Önnheim, Mats Jirstrand, Lennart Svensson,
• Abstract summary: Diffusion models can be parameterised in terms of either a score or an energy function. We propose keeping the score parameterisation and computing an acceptance probability inspired by energy-based models.
• Score: 2.682859657520006
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Diffusion models can be parameterised in terms of either a score or an energy function. An energy parameterisation is appealing since it enables an extended sampling procedure with a Metropolis--Hastings (MH) correction step, based on the change in total energy in the proposed samples. Improved sampling is important for model compositions, where off-the-shelf models are combined with each other, in order to sample from new distributions. For model composition, score-based diffusions have the advantages that they are popular and that many pre-trained models are readily available. However, this parameterisation does not, in general, define an energy, and the MH acceptance probability is therefore unavailable, and generally ill-defined. We propose keeping the score parameterisation and computing an acceptance probability inspired by energy-based models through line integration of the score function. This allows us to reuse existing diffusion models and still combine the reverse process with various Markov-Chain Monte Carlo (MCMC) methods. We evaluate our method using numerical experiments and find that score-parameterised versions of the MCMC samplers can achieve similar improvements to the corresponding energy parameterisation.

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