# Learning on the Manifold: Unlocking Standard Diffusion Transformers with Representation Encoders

arXiv: https://arxiv.org/abs/2602.10099 · HTML: https://mlsanity.com/paper/2602.10099/

## Key facts

- Cited by 13 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 42 of its 44 references that are in the map.
- First posted on arXiv 10 Feb 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 42)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [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)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [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)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [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)
- [Reconstruction vs. Generation: Taming Optimization Dilemma in Latent Diffusion Models](https://mlsanity.com/paper/2501.01423/) (2025)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [Guiding a Diffusion Model with a Bad Version of Itself](https://mlsanity.com/paper/2406.02507/) (2024)
- [Diffusion Transformers with Representation Autoencoders](https://mlsanity.com/paper/2510.11690/) (2025)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [MDTv2: Masked Diffusion Transformer is a Strong Image Synthesizer](https://mlsanity.com/paper/2303.14389/) (2023)
- [REPA-E: Unlocking VAE for End-to-End Tuning with Latent Diffusion Transformers](https://mlsanity.com/paper/2504.10483/) (2025)
- [Scalable Adaptive Computation for Iterative Generation](https://mlsanity.com/paper/2212.11972/) (2022)
- [Fast Training of Diffusion Models with Masked Transformers](https://mlsanity.com/paper/2306.09305/) (2023)
- [SE(3)-Stochastic Flow Matching for Protein Backbone Generation](https://mlsanity.com/paper/2310.02391/) (2023)
- [Riemannian Continuous Normalizing Flows](https://mlsanity.com/paper/2006.10605/) (2020)
- [DDT: Decoupled Diffusion Transformer](https://mlsanity.com/paper/2504.05741/) (2025)

## Built on by (most cited first, 13 of 13)

- [Image Generation with a Sphere Encoder](https://mlsanity.com/paper/2602.15030/) (2026)
- [Aligning Latent Geometry for Spherical Flow Matching in Image Generation](https://mlsanity.com/paper/2605.15193/) (2026)
- [RiT: Vanilla Diffusion Transformers Suffice in Representation Space](https://mlsanity.com/paper/2605.21981/) (2026)
- [Understanding Geometric Representations in Self-Supervised Vision Transformers via Subspace Intervention](https://mlsanity.com/paper/2607.01987/) (2026)
- [Latent Riemannian Flow Matching for Geometry-Grounded 3D Foundation Models](https://mlsanity.com/paper/2607.19120/) (2026)
- [RADAR: Relative Angular Divergence Across Representations](https://mlsanity.com/paper/2605.23028/) (2026)
- [Geometry-Aware Representation Denoising for Robust Multi-view 3D Reconstruction](https://mlsanity.com/paper/2605.26230/) (2026)
- [Diffusion Image Generation with Explicit Modeling of Data Manifold Geometry](https://mlsanity.com/paper/2606.00094/) (2026)
- [STREAM: Stochastic Riemannian Flow Matching with Anisotropic Decoder for Digital Histopathology Image Generation](https://mlsanity.com/paper/2606.07036/) (2026)
- [Orbis 2: A Hierarchical World Model for Driving](https://mlsanity.com/paper/2607.15898/) (2026)
- [X-Rec Technical Report](https://mlsanity.com/paper/2609.29180/) (2026)
- [Sphere Encoder 2](https://mlsanity.com/paper/2610.02208/) (2026)
- [IntactWorld: Joint World Modeling with Intact Features](https://mlsanity.com/paper/2610.11174/) (2026)

## Abstract (arXiv)

Leveraging representation encoders for generative modeling offers a path for efficient, high-fidelity synthesis. However, standard diffusion transformers fail to converge on these representations directly. While recent work attributes this to a capacity bottleneck proposing computationally expensive width scaling of diffusion transformers we demonstrate that the failure is fundamentally geometric. We identify Geometric Interference as the root cause: standard Euclidean flow matching forces probability paths through the low-density interior of the hyperspherical feature space of representation encoders, rather than following the manifold surface. To resolve this, we propose Riemannian Flow Matching with Jacobi Regularization (RJF). By constraining the generative process to the manifold geodesics and correcting for curvature-induced error propagation, RJF enables standard Diffusion Transformer architectures to converge without width scaling. Our method RJF enables the standard DiT-B architecture (131M parameters) to converge effectively, achieving an FID of 3.37 where prior methods fail to converge. Code: https://github.com/amandpkr/RJF