Non-asymptotic convergence bound of conditional diffusion models
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908490174300160 |
|---|---|
| author | Li, Mengze |
| author_facet | Li, Mengze |
| contents | Learning and generating various types of data based on conditional diffusion models has been a research hotspot in recent years. Although conditional diffusion models have made considerable progress in improving acceleration algorithms and enhancing generation quality, the lack of non-asymptotic properties has hindered theoretical research. To address this gap, we focus on a conditional diffusion model within the domains of classification and regression (CARD), which aims to learn the original distribution with given input x (denoted as Y|X). It innovatively integrates a pre-trained model f_ϕ(x) into the original diffusion model framework, allowing it to precisely capture the original conditional distribution given f (expressed as Y|f_ϕ(x)). Remarkably, when f_ϕ(x) performs satisfactorily, Y|f_ϕ(x) closely approximates Y|X. Theoretically, we deduce the stochastic differential equations of CARD and establish its generalized form predicated on the Fokker-Planck equation, thereby erecting a firm theoretical foundation for analysis. Mainly under the Lipschitz assumptions, we utilize the second-order Wasserstein distance to demonstrate the upper error bound between the original and the generated conditional distributions. Additionally, by appending assumptions such as light-tailedness to the original distribution, we derive the convergence upper bound between the true value analogous to the score function and the corresponding network-estimated value. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10944 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-asymptotic convergence bound of conditional diffusion models Li, Mengze Machine Learning Learning and generating various types of data based on conditional diffusion models has been a research hotspot in recent years. Although conditional diffusion models have made considerable progress in improving acceleration algorithms and enhancing generation quality, the lack of non-asymptotic properties has hindered theoretical research. To address this gap, we focus on a conditional diffusion model within the domains of classification and regression (CARD), which aims to learn the original distribution with given input x (denoted as Y|X). It innovatively integrates a pre-trained model f_ϕ(x) into the original diffusion model framework, allowing it to precisely capture the original conditional distribution given f (expressed as Y|f_ϕ(x)). Remarkably, when f_ϕ(x) performs satisfactorily, Y|f_ϕ(x) closely approximates Y|X. Theoretically, we deduce the stochastic differential equations of CARD and establish its generalized form predicated on the Fokker-Planck equation, thereby erecting a firm theoretical foundation for analysis. Mainly under the Lipschitz assumptions, we utilize the second-order Wasserstein distance to demonstrate the upper error bound between the original and the generated conditional distributions. Additionally, by appending assumptions such as light-tailedness to the original distribution, we derive the convergence upper bound between the true value analogous to the score function and the corresponding network-estimated value. |
| title | Non-asymptotic convergence bound of conditional diffusion models |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2508.10944 |