# Generate in Reconstruction Space, Match in Semantic Space: Transport Geometry for One-Step Generation

arXiv: https://arxiv.org/abs/2606.00514 · HTML: https://mlsanity.com/paper/2606.00514/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 46 references that are in the map.
- First posted on arXiv 30 May 2026.

## Builds on (most cited first, 30 of 33)

- [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)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (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)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think](https://mlsanity.com/paper/2410.06940/) (2024)
- [Reconstruction vs. Generation: Taming Optimization Dilemma in Latent Diffusion Models](https://mlsanity.com/paper/2501.01423/) (2025)
- [Deep ViT Features as Dense Visual Descriptors](https://mlsanity.com/paper/2112.05814/) (2021)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Diffusion Transformers with Representation Autoencoders](https://mlsanity.com/paper/2510.11690/) (2025)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [REPA-E: Unlocking VAE for End-to-End Tuning with Latent Diffusion Transformers](https://mlsanity.com/paper/2504.10483/) (2025)
- [Generative Modeling via Drifting](https://mlsanity.com/paper/2602.04770/) (2026)
- [Entropic estimation of optimal transport maps](https://mlsanity.com/paper/2109.12004/) (2021)
- [What matters for Representation Alignment: Global Information or Spatial Structure?](https://mlsanity.com/paper/2512.10794/) (2025)
- [Diffuse and Disperse: Image Generation with Representation Regularization](https://mlsanity.com/paper/2506.09027/) (2025)
- [REPA Works Until It Doesn't: Early-Stopped, Holistic Alignment Supercharges Diffusion Training](https://mlsanity.com/paper/2505.16792/) (2025)
- [Joint Embedding vs Reconstruction: Provable Benefits of Latent Space Prediction for Self Supervised Learning](https://mlsanity.com/paper/2505.12477/) (2025)
- [AlignTok: Aligning Visual Foundation Encoders to Tokenizers for Diffusion Models](https://mlsanity.com/paper/2509.25162/) (2025)
- [One Layer Is Enough: Adapting Pretrained Visual Encoders for Image Generation](https://mlsanity.com/paper/2512.07829/) (2025)

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

- [Are We Overthinking One-Step Generation?](https://mlsanity.com/paper/2610.20331/) (2026)

## Abstract (arXiv)

Generative modeling and self-supervised representation learning (SSL) optimize structurally different objectives: generative training rewards distributional fidelity, while SSL rewards semantic coherence. Yet recent work repeatedly finds that SSL features improve generative training, though the mechanism of this synergy remains unclear. Here, we study the benefits of SSL in generative modeling in the framework of one-step generation where the role of representation is explicit: frozen SSL features are used to match generated samples to real data. We use the Sinkhorn divergence in that feature space, providing a tractable surrogate for the Wasserstein distance, the population-level discrepancy approximated by Fr'echet-style evaluation metrics (such as FID). We find that this objective becomes highly effective when computed in a semantically structured SSL feature space (a 39× reduction in ImageNet FID). We trace this behavior primarily to matching estimation: semantic SSL features that suppress nuisance reconstruction details induce a more compact geometry, making distribution matching more tractable. As a consequence, the best training SSL features need not match the features used by the evaluation metric. In particular, we show that using Inception as the feature extractor can improve FID while degrading matching stability and sample quality, revealing a form of metric hacking. Using extensive experiments on ImageNet, we identify which SSL feature families lead to best generation performance and show that matching stability is a quantitative criterion for selecting them. Code is available at https://github.com/Genentech/semantic-transport-generation.