# Complexity Matters: Rethinking the Latent Space for Generative Modeling

arXiv: https://arxiv.org/abs/2307.08283 · HTML: https://mlsanity.com/paper/2307.08283/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 67 of its 90 references that are in the map.
- First posted on arXiv 17 Jul 2023.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 67)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Scaling Autoregressive Models for Content-Rich Text-to-Image Generation](https://mlsanity.com/paper/2206.10789/) (2022)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Scaling Vision Transformers](https://mlsanity.com/paper/2106.04560/) (2021)

## Built on by (most cited first, 19 of 19)

- [EQ-VAE: Equivariance Regularized Latent Space for Improved Generative Image Modeling](https://mlsanity.com/paper/2502.09509/) (2025)
- [Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connections](https://mlsanity.com/paper/2404.02954/) (2024)
- [Stabilize the Latent Space for Image Autoregressive Modeling: A Unified Perspective](https://mlsanity.com/paper/2410.12490/) (2024)
- [Elucidating The Design Space of Classifier-Guided Diffusion Generation](https://mlsanity.com/paper/2310.11311/) (2023)
- [The Surprising Effectiveness of Skip-Tuning in Diffusion Sampling](https://mlsanity.com/paper/2402.15170/) (2024)
- [FerretNet: Efficient Synthetic Image Detection via Local Pixel Dependencies](https://mlsanity.com/paper/2509.20890/) (2025)
- [PocketSR: The Super-Resolution Expert in Your Pocket Mobiles](https://mlsanity.com/paper/2510.03012/) (2025)
- [Referee Can Play: An Alternative Approach to Conditional Generation via Model Inversion](https://mlsanity.com/paper/2402.16305/) (2024)
- [Vestibular schwannoma growth prediction from longitudinal MRI by time conditioned neural fields](https://mlsanity.com/paper/2404.02614/) (2024)
- [Quantum latent distributions in deep generative models](https://mlsanity.com/paper/2508.19857/) (2025)
- [Kill it with FIRE: On Leveraging Latent Space Directions for Runtime Backdoor Mitigation in Deep Neural Networks](https://mlsanity.com/paper/2602.10780/) (2026)
- [Quantum Down Sampling Filter for Variational Auto-encoder](https://mlsanity.com/paper/2501.06259/) (2025)
- [Anomaly Detection via Autoencoder Composite Features and NCE](https://mlsanity.com/paper/2502.01920/) (2025)
- [Conjuring Positive Pairs for Efficient Unification of Representation Learning and Image Synthesis](https://mlsanity.com/paper/2503.15060/) (2025)
- [MAYA: Addressing Inconsistencies in Generative Password Guessing through a Unified Benchmark](https://mlsanity.com/paper/2504.16651/) (2025)
- [Quantum enhanced ensemble GANs for anomaly detection in continuous biomanufacturing](https://mlsanity.com/paper/2508.21438/) (2025)
- [Beyond Linear Diffusions: Improved Representations for Rare Conditional Generative Modeling](https://mlsanity.com/paper/2510.02499/) (2025)
- [Learning Discrete Autoregressive Priors with Wasserstein Gradient Flow](https://mlsanity.com/paper/2605.06148/) (2026)
- [Symmetric Divergence and Normalized Similarity: A Unified Topological Framework for Representation Analysis](https://mlsanity.com/paper/2606.06342/) (2026)

## Abstract (arXiv)

In generative modeling, numerous successful approaches leverage a low-dimensional latent space, e.g., Stable Diffusion models the latent space induced by an encoder and generates images through a paired decoder. Although the selection of the latent space is empirically pivotal, determining the optimal choice and the process of identifying it remain unclear. In this study, we aim to shed light on this under-explored topic by rethinking the latent space from the perspective of model complexity. Our investigation starts with the classic generative adversarial networks (GANs). Inspired by the GAN training objective, we propose a novel "distance" between the latent and data distributions, whose minimization coincides with that of the generator complexity. The minimizer of this distance is characterized as the optimal data-dependent latent that most effectively capitalizes on the generator's capacity. Then, we consider parameterizing such a latent distribution by an encoder network and propose a two-stage training strategy called Decoupled Autoencoder (DAE), where the encoder is only updated in the first stage with an auxiliary decoder and then frozen in the second stage while the actual decoder is being trained. DAE can improve the latent distribution and as a result, improve the generative performance. Our theoretical analyses are corroborated by comprehensive experiments on various models such as VQGAN and Diffusion Transformer, where our modifications yield significant improvements in sample quality with decreased model complexity.