# Fixed Point Diffusion Models

arXiv: https://arxiv.org/abs/2401.08741 · HTML: https://mlsanity.com/paper/2401.08741/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 38 of its 56 references that are in the map.
- First posted on arXiv 16 Jan 2024.

## Placed in

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

## Builds on (most cited first, 30 of 38)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [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)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://mlsanity.com/paper/1909.11942/) (2019)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [LAION-400M: Open Dataset of CLIP-Filtered 400 Million Image-Text Pairs](https://mlsanity.com/paper/2111.02114/) (2021)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [DataComp: In search of the next generation of multimodal datasets](https://mlsanity.com/paper/2304.14108/) (2023)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Common Diffusion Noise Schedules and Sample Steps are Flawed](https://mlsanity.com/paper/2305.08891/) (2023)
- [Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality](https://mlsanity.com/paper/2202.05830/) (2022)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [Multiscale Deep Equilibrium Models](https://mlsanity.com/paper/2006.08656/) (2020)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2205.15019/) (2022)

## Built on by (most cited first, 16 of 16)

- [Self-conditioned Flow Map Language Models via Fixed-point Flows](https://mlsanity.com/paper/2607.00714/) (2026)
- [Improving Flow Matching by Aligning Flow Divergence](https://mlsanity.com/paper/2602.00869/) (2026)
- [Fixed-Point Masked Generative Modeling](https://mlsanity.com/paper/2605.31215/) (2026)
- [Closed-Loop Long-Horizon Robotic Planning via Equilibrium Sequence Modeling](https://mlsanity.com/paper/2410.01440/) (2024)
- [Certified Robustness for Deep Equilibrium Models via Serialized Random Smoothing](https://mlsanity.com/paper/2411.00899/) (2024)
- [Recursive Scaling in Masked Diffusion Models](https://mlsanity.com/paper/2606.18022/) (2026)
- [Lipschitz Multiscale Deep Equilibrium Models: A Theoretically Guaranteed and Accelerated Approach](https://mlsanity.com/paper/2602.03297/) (2026)
- [Depth through recurrence: Looped transformers for flow-matching TTS](https://mlsanity.com/paper/2609.29768/) (2026)
- [LiFT: Loop Flow Transformers](https://mlsanity.com/paper/2610.05538/) (2026)
- [PoM: A Linear-Time Replacement for Attention with the Polynomial Mixer](https://mlsanity.com/paper/2604.06129/) (2026)
- [Training-free, Perceptually Consistent Low-Resolution Previews with High-Resolution Image for Efficient Workflows of Diffusion Models](https://mlsanity.com/paper/2604.09227/) (2026)
- [Visual Implicit Autoregressive Modeling](https://mlsanity.com/paper/2605.01220/) (2026)
- [Self-Consistent Generative Paths via Admissible Random Variational Transport](https://mlsanity.com/paper/2606.08953/) (2026)
- [Timestep Rescheduling in Diffusion Inversion](https://mlsanity.com/paper/2606.15389/) (2026)
- [Toward a mechanistic understanding of inference in visual cortex and diffusion models](https://mlsanity.com/paper/2607.15693/) (2026)
- [Towards Looped Models Done Right, Part II: Rethinking at Fixed Points](https://mlsanity.com/paper/2610.06833/) (2026)

## Abstract (arXiv)

We introduce the Fixed Point Diffusion Model (FPDM), a novel approach to image generation that integrates the concept of fixed point solving into the framework of diffusion-based generative modeling. Our approach embeds an implicit fixed point solving layer into the denoising network of a diffusion model, transforming the diffusion process into a sequence of closely-related fixed point problems. Combined with a new stochastic training method, this approach significantly reduces model size, reduces memory usage, and accelerates training. Moreover, it enables the development of two new techniques to improve sampling efficiency: reallocating computation across timesteps and reusing fixed point solutions between timesteps. We conduct extensive experiments with state-of-the-art models on ImageNet, FFHQ, CelebA-HQ, and LSUN-Church, demonstrating substantial improvements in performance and efficiency. Compared to the state-of-the-art DiT model, FPDM contains 87% fewer parameters, consumes 60% less memory during training, and improves image generation quality in situations where sampling computation or time is limited. Our code and pretrained models are available at https://lukemelas.github.io/fixed-point-diffusion-models.