Constant-Target Energy Matching: A Unified Framework for Continuous and Discrete Density Estimation
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913107265191936 |
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| author | Zeng, Zhijun Jiang, Yixuan Hu, Pipi Shi, Zuoqiang |
| author_facet | Zeng, Zhijun Jiang, Yixuan Hu, Pipi Shi, Zuoqiang |
| contents | Density estimation is a central primitive in probabilistic modeling, yet continuous, discrete, and mixed-variable domains are often treated by separate objectives, limiting the ability to exploit a common statistical structure across data types. Continuous score-based methods rely on log-density gradients, while discrete extensions typically use concrete score whose unbounded targets become unstable near low-probability states. We introduce Constant-Target Energy Matching (CTEM), a unified energy-based framework for density estimation on general state spaces. CTEM replaces ordinary density-ratio regression with a bounded energy-difference transform and derives from it a sample-only training objective with the constant target 1. The learned scalar potential recovers log p without partition-function estimation or explicit unbounded ratio regression. Across continuous, discrete, and mixed-variable benchmarks, CTEM substantially improves density estimation over competitive baselines and yields higher-quality samples under standard sampling procedures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09085 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Constant-Target Energy Matching: A Unified Framework for Continuous and Discrete Density Estimation Zeng, Zhijun Jiang, Yixuan Hu, Pipi Shi, Zuoqiang Artificial Intelligence Probability 62G07, 68T07, 62H12 G.3; I.2.6 Density estimation is a central primitive in probabilistic modeling, yet continuous, discrete, and mixed-variable domains are often treated by separate objectives, limiting the ability to exploit a common statistical structure across data types. Continuous score-based methods rely on log-density gradients, while discrete extensions typically use concrete score whose unbounded targets become unstable near low-probability states. We introduce Constant-Target Energy Matching (CTEM), a unified energy-based framework for density estimation on general state spaces. CTEM replaces ordinary density-ratio regression with a bounded energy-difference transform and derives from it a sample-only training objective with the constant target 1. The learned scalar potential recovers log p without partition-function estimation or explicit unbounded ratio regression. Across continuous, discrete, and mixed-variable benchmarks, CTEM substantially improves density estimation over competitive baselines and yields higher-quality samples under standard sampling procedures. |
| title | Constant-Target Energy Matching: A Unified Framework for Continuous and Discrete Density Estimation |
| topic | Artificial Intelligence Probability 62G07, 68T07, 62H12 G.3; I.2.6 |
| url | https://arxiv.org/abs/2605.09085 |