# Understanding Flatness in Generative Models: Its Role and Benefits

arXiv: https://arxiv.org/abs/2503.11078 · HTML: https://mlsanity.com/paper/2503.11078/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 39 of its 50 references that are in the map.
- First posted on arXiv 14 Mar 2025.

## Placed in

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

## Builds on (most cited first, 30 of 39)

- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [SWAD: Domain Generalization by Seeking Flat Minima](https://mlsanity.com/paper/2102.08604/) (2021)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks](https://mlsanity.com/paper/2102.11600/) (2021)
- [Q-Diffusion: Quantizing Diffusion Models](https://mlsanity.com/paper/2302.04304/) (2023)
- [Generalized Federated Learning via Sharpness Aware Minimization](https://mlsanity.com/paper/2206.02618/) (2022)
- [Patch Diffusion: Faster and More Data-Efficient Training of Diffusion Models](https://mlsanity.com/paper/2304.12526/) (2023)
- [Overcoming Catastrophic Forgetting in Incremental Few-Shot Learning by Finding Flat Minima](https://mlsanity.com/paper/2111.01549/) (2021)
- [GS-WGAN: A Gradient-Sanitized Approach for Learning Differentially Private Generators](https://mlsanity.com/paper/2006.08265/) (2020)
- [Elucidating the Exposure Bias in Diffusion Models](https://mlsanity.com/paper/2308.15321/) (2023)
- [Improving Generalization in Federated Learning by Seeking Flat Minima](https://mlsanity.com/paper/2203.11834/) (2022)
- [Input Perturbation Reduces Exposure Bias in Diffusion Models](https://mlsanity.com/paper/2301.11706/) (2023)
- [PTQ4DiT: Post-training Quantization for Diffusion Transformers](https://mlsanity.com/paper/2405.16005/) (2024)

## Built on by (most cited first, 3 of 3)

- [Sparsity-Driven Plasticity in Multi-Task Reinforcement Learning](https://mlsanity.com/paper/2508.06871/) (2025)
- [Reward Sharpness-Aware Fine-Tuning for Diffusion Models](https://mlsanity.com/paper/2603.21175/) (2026)
- [Neural Network Quantization by Learning Low-Loss Subspaces](https://mlsanity.com/paper/2606.25087/) (2026)

## Abstract (arXiv)

Flat minima, known to enhance generalization and robustness in supervised learning, remain largely unexplored in generative models. In this work, we systematically investigate the role of loss surface flatness in generative models, both theoretically and empirically, with a particular focus on diffusion models. We establish a theoretical claim that flatter minima improve robustness against perturbations in target prior distributions, leading to benefits such as reduced exposure bias -- where errors in noise estimation accumulate over iterations -- and significantly improved resilience to model quantization, preserving generative performance even under strong quantization constraints. We further observe that Sharpness-Aware Minimization (SAM), which explicitly controls the degree of flatness, effectively enhances flatness in diffusion models even surpassing the indirectly promoting flatness methods -- Input Perturbation (IP) which enforces the Lipschitz condition, ensembling-based approach like Stochastic Weight Averaging (SWA) and Exponential Moving Average (EMA) -- are less effective. Through extensive experiments on CIFAR-10, LSUN Tower, and FFHQ, we demonstrate that flat minima in diffusion models indeed improve not only generative performance but also robustness.