# CrossFlow: One-Step Generation Across Latent and Pixel Spaces

arXiv: https://arxiv.org/abs/2606.19970 · HTML: https://mlsanity.com/paper/2606.19970/

## Key facts

- Cited by 2 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 48 of its 57 references that are in the map.
- First posted on arXiv 18 Jun 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 48)

- [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)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [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)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think](https://mlsanity.com/paper/2410.06940/) (2024)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [StyleGAN-XL: Scaling StyleGAN to Large Diverse Datasets](https://mlsanity.com/paper/2202.00273/) (2022)
- [Scaling up GANs for Text-to-Image Synthesis](https://mlsanity.com/paper/2303.05511/) (2023)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023)
- [Muon is Scalable for LLM Training](https://mlsanity.com/paper/2502.16982/) (2025)
- [Simple diffusion: End-to-end diffusion for high resolution images](https://mlsanity.com/paper/2301.11093/) (2023)

## Built on by (most cited first, 2 of 2)

- [An Empirical Study of Training Pixel-Space Text-to-Image Diffusion Models](https://mlsanity.com/paper/2608.16887/) (2026)
- [Latent Space Is Not Flat: Rethinking Latent Structure for 3D Medical Image Synthesis](https://mlsanity.com/paper/2609.32794/) (2026)

## Abstract (arXiv)

Most diffusion and flow-matching generators define the prior, probability path, and prediction target in the same representation space. Latent diffusion improves efficiency by moving this path into an autoencoder latent space, but the final sample is still produced by a separately trained decoder. This separation creates a mismatch: the generator is optimized for latent-space prediction, while final quality depends on how the decoder handles generated latents that may differ from clean encoder outputs. We introduce CrossFlow, a cross-space flow formulation that maps noisy latent inputs directly to pixel-space images. The key technical step is a velocity-free one-step objective: the latent trajectory defines the training path, but the supervised prediction is an image rather than a latent displacement. This lets one model act both as a one-step latent-to-pixel generator and as a decoder replacement for latent diffusion pipelines. On class-conditional ImageNet-1k at 256×256, CrossFlow-XL achieves 1.62 FID with one function evaluation. Ablations show that the latent encoder and pixel-space perceptual and adversarial losses are important for fidelity. These results indicate that cross-space flow objectives can combine the efficiency of latent representations with direct pixel-space supervision, without requiring a separate decoder at inference.