# Cloud Model Characteristic Function Auto-Encoder: Integrating Cloud Model Theory with MMD Regularization for Enhanced Generative Modeling

arXiv: https://arxiv.org/abs/2508.04447 · HTML: https://mlsanity.com/paper/2508.04447/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 36 references that are in the map.
- First posted on arXiv 6 Aug 2025.

## Builds on (most cited first, 17 of 17)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [Composing graphical models with neural networks for structured representations and fast inference](https://mlsanity.com/paper/1603.06277/) (2016)
- [Stick-Breaking Variational Autoencoders](https://mlsanity.com/paper/1605.06197/) (2016)
- [Improving Variational Auto-Encoders using Householder Flow](https://mlsanity.com/paper/1611.09630/) (2016)
- [From optimal transport to generative modeling: the VEGAN cookbook](https://mlsanity.com/paper/1705.07642/) (2017)
- [Sliced-Wasserstein Autoencoder: An Embarrassingly Simple Generative Model](https://mlsanity.com/paper/1804.01947/) (2018)
- [On Error Propagation of Diffusion Models](https://mlsanity.com/paper/2308.05021/) (2023)
- [Slot-VAE: Object-Centric Scene Generation with Slot Attention](https://mlsanity.com/paper/2306.06997/) (2023)
- [Fast Inference in Denoising Diffusion Models via MMD Finetuning](https://mlsanity.com/paper/2301.07969/) (2023)
- [Generative neural networks for characteristic functions](https://mlsanity.com/paper/2401.04778/) (2024)

## Abstract (arXiv)

We introduce Cloud Model Characteristic Function Auto-Encoder (CMCFAE), a novel generative model that integrates the cloud model into the Wasserstein Auto-Encoder (WAE) framework. By leveraging the characteristic functions of the cloud model to regularize the latent space, our approach enables more accurate modeling of complex data distributions. Unlike conventional methods that rely on a standard Gaussian prior and traditional divergence measures, our method employs a cloud model prior, providing a more flexible and realistic representation of the latent space, thus mitigating the homogenization observed in reconstructed samples. We derive the characteristic function of the cloud model and propose a corresponding regularizer within the WAE framework. Extensive quantitative and qualitative evaluations on MNIST, FashionMNIST, CIFAR-10, and CelebA demonstrate that CMCFAE outperforms existing models in terms of reconstruction quality, latent space structuring, and sample diversity. This work not only establishes a novel integration of cloud model theory with MMD-based regularization but also offers a promising new perspective for enhancing autoencoder-based generative models.