# CINDES: Classification induced neural density estimator and simulator

arXiv: https://arxiv.org/abs/2510.00367 · HTML: https://mlsanity.com/paper/2510.00367/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 54 references that are in the map.
- First posted on arXiv 1 Oct 2025.

## Builds on (most cited first, 22 of 22)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023)
- [A Phase Transition in Diffusion Models Reveals the Hierarchical Nature of Data](https://mlsanity.com/paper/2402.16991/) (2024)
- [How Well Generative Adversarial Networks Learn Distributions](https://mlsanity.com/paper/1811.03179/) (2018)
- [An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization](https://mlsanity.com/paper/2404.07771/) (2024)
- [Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorial](https://mlsanity.com/paper/2402.07487/) (2024)
- [Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality](https://mlsanity.com/paper/2410.18784/) (2024)
- [Factor Augmented Sparse Throughput Deep ReLU Neural Networks for High Dimensional Regression](https://mlsanity.com/paper/2210.02002/) (2022)
- [How do noise tails impact on deep ReLU networks?](https://mlsanity.com/paper/2203.10418/) (2022)
- [Deep Neural Networks for Nonparametric Interaction Models with Diverging Dimension](https://mlsanity.com/paper/2302.05851/) (2023)
- [LinCDE: Conditional Density Estimation via Lindsey's Method](https://mlsanity.com/paper/2107.12713/) (2021)
- [Nonparametric estimation of a factorizable density using diffusion models](https://mlsanity.com/paper/2501.01783/) (2025)
- [Causality Pursuit from Heterogeneous Environments via Neural Adversarial Invariance Learning](https://mlsanity.com/paper/2405.04715/) (2024)
- [Dimension-independent rates for structured neural density estimation](https://mlsanity.com/paper/2411.15095/) (2024)

## Built on by (most cited first, 1 of 1)

- [Tweedie's Formulae and Diffusion Generative Models Beyond Gaussian](https://mlsanity.com/paper/2605.19391/) (2026)

## Abstract (arXiv)

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.