# Moment- and Power-Spectrum-Based Gaussianity Regularization for Text-to-Image Models

arXiv: https://arxiv.org/abs/2509.07027 · HTML: https://mlsanity.com/paper/2509.07027/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 38 references that are in the map.
- First posted on arXiv 7 Sep 2025.

## Builds on (most cited first, 21 of 21)

- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Pick-a-Pic: An Open Dataset of User Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2305.01569/) (2023)
- [Human Preference Score v2: A Solid Benchmark for Evaluating Human Preferences of Text-to-Image Synthesis](https://mlsanity.com/paper/2306.09341/) (2023)
- [Diffusion Model Alignment Using Direct Preference Optimization](https://mlsanity.com/paper/2311.12908/) (2023)
- [Directly Fine-Tuning Diffusion Models on Differentiable Rewards](https://mlsanity.com/paper/2309.17400/) (2023)
- [PixArt-Sigma: Weak-to-Strong Training of Diffusion Transformer for 4K Text-to-Image Generation](https://mlsanity.com/paper/2403.04692/) (2024)
- [Aligning Text-to-Image Diffusion Models with Reward Backpropagation](https://mlsanity.com/paper/2310.03739/) (2023)
- [T2I-CompBench++: An Enhanced and Comprehensive Benchmark for Compositional Text-to-image Generation](https://mlsanity.com/paper/2307.06350/) (2023)
- [Using Human Feedback to Fine-tune Diffusion Models without Any Reward Model](https://mlsanity.com/paper/2311.13231/) (2023)
- [D-Flow: Differentiating through Flows for Controlled Generation](https://mlsanity.com/paper/2402.14017/) (2024)
- [ReNO: Enhancing One-step Text-to-Image Models through Reward-based Noise Optimization](https://mlsanity.com/paper/2406.04312/) (2024)
- [Optimizing Diffusion Noise Can Serve As Universal Motion Priors](https://mlsanity.com/paper/2312.11994/) (2023)
- [DartControl: A Diffusion-Based Autoregressive Motion Model for Real-Time Text-Driven Motion Control](https://mlsanity.com/paper/2410.05260/) (2024)
- [Robust Quantization: One Model to Rule Them All](https://mlsanity.com/paper/2002.07686/) (2020)
- [Norm-guided latent space exploration for text-to-image generation](https://mlsanity.com/paper/2306.08687/) (2023)
- [On the training dynamics of deep networks with L2 regularization](https://mlsanity.com/paper/2006.08643/) (2020)
- [Aligning Language Models with Demonstrated Feedback](https://mlsanity.com/paper/2406.00888/) (2024)

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

- [Gradient Preconditioning for Efficient and Reliable Reward-Guided Generation](https://mlsanity.com/paper/2602.08646/) (2026)
- [InverFill: One-Step Inversion for Enhanced Few-Step Diffusion Inpainting](https://mlsanity.com/paper/2603.23463/) (2026)
- [StressDream: Steering Video World Models for Robust Policy Evaluation and Improvement](https://mlsanity.com/paper/2606.00267/) (2026)

## Abstract (arXiv)

We propose a novel regularization loss that enforces standard Gaussianity, encouraging samples to align with a standard Gaussian distribution. This facilitates a range of downstream tasks involving optimization in the latent space of text-to-image models. We treat elements of a high-dimensional sample as one-dimensional standard Gaussian variables and define a composite loss that combines moment-based regularization in the spatial domain with power spectrum-based regularization in the spectral domain. Since the expected values of moments and power spectrum distributions are analytically known, the loss promotes conformity to these properties. To ensure permutation invariance, the losses are applied to randomly permuted inputs. Notably, existing Gaussianity-based regularizations fall within our unified framework: some correspond to moment losses of specific orders, while the previous covariance-matching loss is equivalent to our spectral loss but incurs higher time complexity due to its spatial-domain computation. We showcase the application of our regularization in generative modeling for test-time reward alignment with a text-to-image model, specifically to enhance aesthetics and text alignment. Our regularization outperforms previous Gaussianity regularization, effectively prevents reward hacking and accelerates convergence.