# LiFT: Loop Flow Transformers

arXiv: https://arxiv.org/abs/2610.05538 · HTML: https://mlsanity.com/paper/2610.05538/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 32 of its 34 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 32)

- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Cosmos World Foundation Model Platform for Physical AI](https://mlsanity.com/paper/2501.03575/) (2025)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Movie Gen: A Cast of Media Foundation Models](https://mlsanity.com/paper/2410.13720/) (2024)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [Inference-Time Scaling for Diffusion Models beyond Scaling Denoising Steps](https://mlsanity.com/paper/2501.09732/) (2025)
- [Scalable Adaptive Computation for Iterative Generation](https://mlsanity.com/paper/2212.11972/) (2022)
- [Can You Learn an Algorithm? Generalizing from Easy to Hard Problems with Recurrent Networks](https://mlsanity.com/paper/2106.04537/) (2021)
- [Restart Sampling for Improving Generative Processes](https://mlsanity.com/paper/2306.14878/) (2023)
- [One-Step Diffusion Distillation via Deep Equilibrium Models](https://mlsanity.com/paper/2401.08639/) (2023)
- [LoopFormer: Elastic-Depth Looped Transformers for Latent Reasoning via Shortcut Modulation](https://mlsanity.com/paper/2602.11451/) (2026)
- [On Expressive Power of Looped Transformers: Theoretical Analysis and Enhancement via Timestep Encoding](https://mlsanity.com/paper/2410.01405/) (2024)
- [How Much Is One Recurrence Worth? Iso-Depth Scaling Laws for Looped Language Models](https://mlsanity.com/paper/2604.21106/) (2026)
- [Fixed Point Diffusion Models](https://mlsanity.com/paper/2401.08741/) (2024)
- [ELT: Elastic Looped Transformers for Visual Generation](https://mlsanity.com/paper/2604.09168/) (2026)
- [DiT-Air: Revisiting the Efficiency of Diffusion Model Architecture Design in Text to Image Generation](https://mlsanity.com/paper/2503.10618/) (2025)
- [Deeply Supervised Flow-Based Generative Models](https://mlsanity.com/paper/2503.14494/) (2025)
- [Thinking with Looped Flows](https://mlsanity.com/paper/2609.11801/) (2026)
- [Flow Reasoning Models: Turning Flows Into Efficient Recurrent Reasoners](https://mlsanity.com/paper/2606.29150/) (2026)
- [Fixed-Point Masked Generative Modeling](https://mlsanity.com/paper/2605.31215/) (2026)
- [Speedrunning ImageNet Diffusion](https://mlsanity.com/paper/2512.12386/) (2025)
- [Recursive Scaling in Masked Diffusion Models](https://mlsanity.com/paper/2606.18022/) (2026)
- [How Model Growth, Recursion, and Boundary Operators Influence Scaling Exponents](https://mlsanity.com/paper/2609.19107/) (2026)
- [ODEt(ODEl): Shortcutting the Time and the Length in Diffusion and Flow Models for Faster Sampling](https://mlsanity.com/paper/2506.21714/) (2025)

## Built on by (most cited first, 1 of 1)

- [Coarse-Graining Recursive Expert Computation: Continuation-Relative Interfaces and Failure Modes](https://mlsanity.com/paper/2610.14413/) (2026)

## Abstract (arXiv)

We introduce Loop Flow Transformers (LiFT), a family of looped generative models that scales computation by repeatedly applying a shared Diffusion Transformer (DiT) core, with only light changes to the standard architecture. Rather than asking every recurrent step for the final prediction, LiFT trains each step with a single regression target: a point on a straight path from the model's initial estimate to the flow-matching target. Because we index these targets by a continuous depth coordinate, a trained model can loop far beyond its training depth with no retraining, early exits, or other modifications. In our experiments, these longer rollouts improve generation, so inference computation can grow without adding parameters. On ImageNet at 256x256, LiFT-L/2 achieves an FID 3.34 points lower than our dense DiT-XL/2 baseline while using approximately 60% fewer parameters, 32% fewer training FLOPs, and 52% fewer inference FLOPs.