# SPARE: Structural Parameter-Free Affinity Regularization for Flow Matching

arXiv: https://arxiv.org/abs/2608.01990 · HTML: https://mlsanity.com/paper/2608.01990/

## 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 22 of its 32 references that are in the map.
- First posted on arXiv 3 Aug 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, 22 of 22)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [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)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (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)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Relational Knowledge Distillation](https://mlsanity.com/paper/1904.05068/) (2019)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Similarity-Preserving Knowledge Distillation](https://mlsanity.com/paper/1907.09682/) (2019)
- [Generating Images with Sparse Representations](https://mlsanity.com/paper/2103.03841/) (2021)
- [ReSSL: Relational Self-Supervised Learning with Weak Augmentation](https://mlsanity.com/paper/2107.09282/) (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)
- [No Other Representation Component Is Needed: Diffusion Transformers Can Provide Representation Guidance by Themselves](https://mlsanity.com/paper/2505.02831/) (2025)
- [SRA 2: Variational Autoencoder Self-Representation Alignment for Efficient Diffusion Training](https://mlsanity.com/paper/2601.17830/) (2026)
- [No Alignment Needed for Generation: Learning Linearly Separable Representations in Diffusion Models](https://mlsanity.com/paper/2509.21565/) (2025)
- [DiverseDiT: Towards Diverse Representation Learning in Diffusion Transformers](https://mlsanity.com/paper/2603.04239/) (2026)
- [AHPA: Adaptive Hierarchical Prior Alignment for Diffusion Transformers](https://mlsanity.com/paper/2605.03317/) (2026)
- [Beyond Point-Wise Matching: Structural Representation Alignment for Accelerating Diffusion Transformers](https://mlsanity.com/paper/2605.16949/) (2026)

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

- [What Visual Generators Need from Teachers: Rethinking Representation Alignment](https://mlsanity.com/paper/2609.34732/) (2026)

## Abstract (arXiv)

Denoising diffusion transformers achieve strong generation quality but converge slowly during training. Regularizing their internal representations has emerged as an effective accelerator, yet existing methods split into two families with complementary costs. Target-based methods strengthen representations by aligning them to external features, which requires an external encoder and a learnable projection head to bridge feature spaces. Target-free methods hold no reference at all, and can only repel the model's own features across samples or layers, discarding whatever structure the data contains. Prior work suggests that spatial structure, rather than global semantics, drives the gains of alignment. We therefore ask whether such structure can serve as a target directly, and whether it exists not only within an image but across images. Our key insight is that the clean data latent already carries this structure in the relations among its tokens, where a relation is the similarity between two tokens, a single scalar comparable across feature spaces without a projection head. We propose Structural Parameter-free Affinity Regularization (SPARE), a regularizer that matches the pairwise affinities of intermediate tokens to those of the clean latents. To exploit this structure fully, SPARE extends the matching to token pairs across images, precisely the pairs that prior target-free methods repel by default, and calibrates both relation types with a single learning objective. On ImageNet 256 × 256 with SiT backbones under matched 400K-iteration budgets, SPARE adds no encoder, head, or parameters and only 0.08 GB of training memory, yet attains the lowest FID among parameter-free regularizers in every tested setting, recovers 37 to 54% of REPA's FID reduction, and improves over REPA when combined with it, reaching FID 1.90 under classifier-free guidance at 1M iterations.