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

Flow matching with $x$-prediction -- regressing the clean data point rather than the ambient velocity -- is known to exploit low-dimensional manifold structure effectively in pixel space \cite{li2025back}. We ask whether a pretrained representation space, while containing a low-dimensional data manifold of comparable intrinsic dimensionality, offers a distribution more favorable for flow-matching learning. Comparing pixel, SD-VAE, and DINOv2 features along four geometric axes, we find that pixel and DINOv2 share nearly identical intrinsic dimensionalities (both $\hat{d}\!\approx\!33$) yet DINOv2 exhibits $7.3\times$ higher effective rank, $35\times$ better covariance conditioning, $11.5\times$ lower excess kurtosis, and $1.7\times$ lower on-manifold interpolation error; SD-VAE latents are consistently intermediate, indicating that the advantage stems from representation-learning objectives rather than mere compression. These statistical properties render the flow-matching regression well-conditioned and remove the need for the specialized prediction heads or Riemannian transport used by prior DINOv2 diffusion methods. We propose the \emph{Representation Image Transformer} (RiT): a vanilla Diffusion Transformer trained by $x$-prediction on frozen DINOv2 features, augmented only by a dimension-aware noise schedule and joint \texttt{[CLS]}-patch modeling. On ImageNet $256{\times}256$, RiT attains FID 1.45 without guidance and 1.14 with classifier-free guidance, outperforming DiT$^\text{DH}$-XL with $19\%$ fewer parameters (676M vs.\ 839M). The resulting ODE is efficiently solvable at coarse discretizations: with classifier-free guidance, $5$ Heun steps already reach FID 2.0 and $10$ steps reach 1.25, without distillation or consistency training. Code at https://github.com/lezhang7/RiT.

Image generative models aim to sample data points from the underlying data manifold, a task that requires learning and decoding a dense, low-dimensional, and compact parameterization space. To achieve this, we propose the Data Manifold-aware Image diffusioN moDel (MIND), a novel framework that explicitly models manifold geometry by integrating discrete patch tokenization into the score function of a continuous diffusion model. This approach successfully leverages both the structural quantification capabilities of discrete tokens and the parallel generation flexibility of continuous diffusion. Moreover, we enable end-to-end differentiable training via a novel soft top-$k$ aggregation mechanism and introduce dual-branch high-frequency feature embedding layers to alleviate the spectral bias of transformer backbones on low-dimensional inputs. Furthermore, for inference, we design a multi-stage transition sampling scheme that dynamically adjusts the sampling scheme based on timestep. Extensive experiments on ImageNet 256$\times$256 demonstrate the effectiveness of MIND. After 80-epoch training, our base model achieves an FID of 22.73 without guidance, nearly halving the 43.47 FID of the vanilla DiT-B/2 baseline. The proposed method reduces FID by 15.95 and 9.06 on average compared with the baselines DiT and SiT, respectively. For image generation on ImageNet-256$\times$256 with guidance, the proposed MIND-B with only 130M parameters achieves an FID of 2.06, superpassing the LlamaGen-3B with 3.1B parameters. The proposed MIND-XL with 715M parameters further reduces the FID to 1.95. Our MIND introduces a fresh perspective on diffusion-based image generation, paving the way for future research and innovation in this community. The code will be publicly available.

We propose SpectralDiT, a lightweight modification to flow-matching Diffusion Transformers that adds timestep-conditioned spectral correction to the MLP residual branch. The module decomposes each residual update into low- and high-frequency components on the patch-token grid, then learns a zero-initialized additive gate so the model initially matches the baseline DiT. On CIFAR-10 pixel-space generation, SpectralDiT improves FID from 20.78 to 19.71 at patch size 1 and reduces the radial Fourier spectrum gap. Furthermore, we scale our method to latent diffusion on ImageNet-100. With 0.6% additional theoretical FLOPs and 1.36% additional parameters, SpectralDiT improves latent flow-matching, achieving an 8.7% relative FID reduction under classifier-free guidance (CFG 2.0). All reported results are averaged over five seeds. Ablations and gate visualizations on CIFAR-10 reveal stable block-specific spectral correction patterns.