提出可自适应加速的神经密度估计器，提升生成模型效率
CINDES: Classification induced neural density estimator and simulator
- 用结构无关方法实现简单可靠的密度估计
- 当真实密度具低维结构时，收敛速度显著更快
- 可无缝接入扩散模型，适合追求高效生成的研究者
基于神经网络的(无)条件密度估计近期受到广泛关注，多种神经密度估计器在真实数据实验中表现优于传统方法。然而，实际应用中仍需确保非负性和单位质量约束，且理论理解有限。特别是，当真实密度具有低维结构时，现有方法能否自适应实现更快收敛率尚不明确。本文提出一种结构无关的神经密度估计器，具备(1)实现简单、(2)理论上可自适应的优势，在真实密度具有低维组合结构时能实现更快收敛。另一关键贡献是证明该估计器可自然融入生成采样流程，尤其在基于得分的扩散模型中，当底层密度具结构性时可实现可证明更快收敛。通过大量模拟和真实数据应用验证了其性能。
原文摘要 · Abstract (English)
Neural network-based methods for (un)conditional density estimation have recently gained substantial attention, as various neural density estimators have outperformed classical approaches in real-data experiments. Despite these empirical successes, implementation can be challenging due to the need to ensure non-negativity and unit-mass constraints, and theoretical understanding remains limited. In particular, it is unclear whether such estimators can adaptively achieve faster convergence rates when the underlying density exhibits a low-dimensional structure. This paper addresses these gaps by proposing a structure-agnostic neural density estimator that is (i) straightforward to implement and (ii) provably adaptive, attaining faster rates when the true density admits a low-dimensional composition structure. Another key contribution of our work is to show that the proposed estimator integrates naturally into generative sampling pipelines, most notably score-based diffusion models, where it achieves provably faster convergence when the underlying density is structured. We validate its performance through extensive simulations and a real-data application.
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