Error bounds for flow matching methods
<p>Score-based generative models are a popular class of generative modelling techniques relying on stochastic differential equations (SDE). From their inception, it was realized that it was also possible to perform generation using ordinary differential equations (ODE) rather than SDE. This le...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Transactions on Machine Learning Research
2024
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| _version_ | 1826312871216152576 |
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| author | Benton, J Deligiannidis, G Doucet, A |
| author_facet | Benton, J Deligiannidis, G Doucet, A |
| author_sort | Benton, J |
| collection | OXFORD |
| description | <p>Score-based generative models are a popular class of generative modelling techniques relying on stochastic differential equations (SDE). From their inception, it was realized that it was also possible to perform generation using ordinary differential equations (ODE) rather than SDE. This led to the introduction of the probability flow ODE approach and denoising diffusion implicit models. Flow matching methods have recently further extended these ODE-based approaches and approximate a flow between two arbitrary probability distributions. Previous work derived bounds on the approximation error of diffusion models under the stochastic sampling regime, given assumptions on the <em>L</em><sup>2</sup> loss. We present error bounds for the flow matching procedure using fully deterministic sampling, assuming an <em>L</em><sup>2</sup> bound on the approximation error and a certain regularity condition on the data distributions.</p> |
| first_indexed | 2024-03-07T08:23:19Z |
| format | Journal article |
| id | oxford-uuid:8132c98e-616f-42d6-b522-8bb8f0b41d6b |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:03:42Z |
| publishDate | 2024 |
| publisher | Transactions on Machine Learning Research |
| record_format | dspace |
| spelling | oxford-uuid:8132c98e-616f-42d6-b522-8bb8f0b41d6b2024-05-08T10:23:24ZError bounds for flow matching methodsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:8132c98e-616f-42d6-b522-8bb8f0b41d6bEnglishSymplectic ElementsTransactions on Machine Learning Research2024Benton, JDeligiannidis, GDoucet, A<p>Score-based generative models are a popular class of generative modelling techniques relying on stochastic differential equations (SDE). From their inception, it was realized that it was also possible to perform generation using ordinary differential equations (ODE) rather than SDE. This led to the introduction of the probability flow ODE approach and denoising diffusion implicit models. Flow matching methods have recently further extended these ODE-based approaches and approximate a flow between two arbitrary probability distributions. Previous work derived bounds on the approximation error of diffusion models under the stochastic sampling regime, given assumptions on the <em>L</em><sup>2</sup> loss. We present error bounds for the flow matching procedure using fully deterministic sampling, assuming an <em>L</em><sup>2</sup> bound on the approximation error and a certain regularity condition on the data distributions.</p> |
| spellingShingle | Benton, J Deligiannidis, G Doucet, A Error bounds for flow matching methods |
| title | Error bounds for flow matching methods |
| title_full | Error bounds for flow matching methods |
| title_fullStr | Error bounds for flow matching methods |
| title_full_unstemmed | Error bounds for flow matching methods |
| title_short | Error bounds for flow matching methods |
| title_sort | error bounds for flow matching methods |
| work_keys_str_mv | AT bentonj errorboundsforflowmatchingmethods AT deligiannidisg errorboundsforflowmatchingmethods AT douceta errorboundsforflowmatchingmethods |