# A new perspective on probabilistic image modeling

arXiv: https://arxiv.org/abs/2203.11034 · HTML: https://mlsanity.com/paper/2203.11034/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 32 references that are in the map.
- First posted on arXiv 21 Mar 2022.

## Builds on (most cited first, 12 of 12)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Einsum Networks: Fast and Scalable Learning of Tractable Probabilistic Circuits](https://mlsanity.com/paper/2004.06231/) (2020)
- [On GANs and GMMs](https://mlsanity.com/paper/1805.12462/) (2018)
- [Deep Gaussian Mixture Models](https://mlsanity.com/paper/1711.06929/) (2017)
- [Fine-Tuning DARTS for Image Classification](https://mlsanity.com/paper/2006.09042/) (2020)
- [Gradient-based training of Gaussian Mixture Models for High-Dimensional Streaming Data](https://mlsanity.com/paper/1912.09379/) (2019)
- [Image Modeling with Deep Convolutional Gaussian Mixture Models](https://mlsanity.com/paper/2104.12686/) (2021)

## Built on by (most cited first, 2 of 2)

- [Adiabatic replay for continual learning](https://mlsanity.com/paper/2303.13157/) (2023)
- [SiamMM: A Mixture Model Perspective on Deep Unsupervised Learning](https://mlsanity.com/paper/2511.05462/) (2025)

## Abstract (arXiv)

We present the Deep Convolutional Gaussian Mixture Model (DCGMM), a new probabilistic approach for image modeling capable of density estimation, sampling and tractable inference. DCGMM instances exhibit a CNN-like layered structure, in which the principal building blocks are convolutional Gaussian Mixture (cGMM) layers. A key innovation w.r.t. related models like sum-product networks (SPNs) and probabilistic circuits (PCs) is that each cGMM layer optimizes an independent loss function and therefore has an independent probabilistic interpretation. This modular approach permits intervening transformation layers to harness the full spectrum of (potentially non-invertible) mappings available to CNNs, e.g., max-pooling or half-convolutions. DCGMM sampling and inference are realized by a deep chain of hierarchical priors, where a sample generated by a given cGMM layer defines the parameters of sampling in the next-lower cGMM layer. For sampling through non-invertible transformation layers, we introduce a new gradient-based sharpening technique that exploits redundancy (overlap) in, e.g., half-convolutions. DCGMMs can be trained end-to-end by SGD from random initial conditions, much like CNNs. We show that DCGMMs compare favorably to several recent PC and SPN models in terms of inference, classification and sampling, the latter particularly for challenging datasets such as SVHN. We provide a public TF2 implementation.