统一处理连续与离散数据的密度估计，提升建模精度与采样质量。
Constant-Target Energy Matching: A Unified Framework for Continuous and Discrete Density Estimation
- 用有界能量差替换传统密度比回归，实现统一建模。
- 样本训练目标恒定为1，避免低概率区域不稳定问题。
- 适用于混合变量场景，采样质量优于现有方法。
密度估计是概率建模的核心任务，但连续、离散及混合变量领域常采用不同目标函数，难以共享统计结构。连续方法依赖对数密度梯度，离散扩展通常使用无界的目标，导致低概率状态附近不稳定。本文提出常目标能量匹配（CTEM），一种适用于一般状态空间的统一能量基密度估计框架。CTEM以有界能量差变换替代常规密度比回归，并推导出仅需样本的训练目标，其目标值恒为1。学习到的标量势能可直接恢复对数似然，无需归一化常数估计或显式无界比值回归。在连续、离散及混合变量基准上，CTEM显著优于竞争基线，且在标准采样流程下生成更高质量样本。
原文摘要 · Abstract (English)
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.
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