# Beyond Fixed Formulas: Data-Driven Linear Predictor for Efficient Diffusion Models

arXiv: https://arxiv.org/abs/2604.26365 · HTML: https://mlsanity.com/paper/2604.26365/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 31 of its 39 references that are in the map.
- First posted on arXiv 29 Apr 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 31)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [CogVideoX: Text-to-Video Diffusion Models with An Expert Transformer](https://mlsanity.com/paper/2408.06072/) (2024)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [HunyuanVideo: A Systematic Framework For Large Video Generative Models](https://mlsanity.com/paper/2412.03603/) (2024)
- [Qwen-Image Technical Report](https://mlsanity.com/paper/2508.02324/) (2025)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [DeepCache: Accelerating Diffusion Models for Free](https://mlsanity.com/paper/2312.00858/) (2023)
- [Timestep Embedding Tells: It's Time to Cache for Video Diffusion Model](https://mlsanity.com/paper/2411.19108/) (2024)
- [Delta-DiT: A Training-Free Acceleration Method Tailored for Diffusion Transformers](https://mlsanity.com/paper/2406.01125/) (2024)
- [Accelerating Diffusion Transformers with Token-wise Feature Caching](https://mlsanity.com/paper/2410.05317/) (2024)
- [Learning-to-Cache: Accelerating Diffusion Transformer via Layer Caching](https://mlsanity.com/paper/2406.01733/) (2024)
- [From Reusing to Forecasting: Accelerating Diffusion Models with TaylorSeers](https://mlsanity.com/paper/2503.06923/) (2025)
- [DiTFastAttn: Attention Compression for Diffusion Transformer Models](https://mlsanity.com/paper/2406.08552/) (2024)
- [Adaptive Caching for Faster Video Generation with Diffusion Transformers](https://mlsanity.com/paper/2411.02397/) (2024)
- [PeRFlow: Piecewise Rectified Flow as Universal Plug-and-Play Accelerator](https://mlsanity.com/paper/2405.07510/) (2024)
- [DiP-GO: A Diffusion Pruner via Few-step Gradient Optimization](https://mlsanity.com/paper/2410.16942/) (2024)
- [Token Pruning for Caching Better: 9 Times Acceleration on Stable Diffusion for Free](https://mlsanity.com/paper/2501.00375/) (2024)
- [SpeCa: Accelerating Diffusion Transformers with Speculative Feature Caching](https://mlsanity.com/paper/2509.11628/) (2025)
- [Rethinking Token-wise Feature Caching: Accelerating Diffusion Transformers with Dual Feature Caching](https://mlsanity.com/paper/2412.18911/) (2024)
- [Forecast then Calibrate: Feature Caching as ODE for Efficient Diffusion Transformers](https://mlsanity.com/paper/2508.16211/) (2025)
- [FreqCa: Accelerating Diffusion Models via Frequency-Aware Caching](https://mlsanity.com/paper/2510.08669/) (2025)
- [HarmoniCa: Harmonizing Training and Inference for Better Feature Caching in Diffusion Transformer Acceleration](https://mlsanity.com/paper/2410.01723/) (2024)
- [Cached Adaptive Token Merging: Dynamic Token Reduction and Redundant Computation Elimination in Diffusion Model](https://mlsanity.com/paper/2501.00946/) (2025)
- [A Survey on Cache Methods in Diffusion Models: Toward Efficient Multi-Modal Generation](https://mlsanity.com/paper/2510.19755/) (2025)

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

- [The Golden Path Hypothesis: Reusable Schedules in Diffusion Caching](https://mlsanity.com/paper/2609.39343/) (2026)
- [Koopman Observers for Diffusion Acceleration: Correcting Feature Forecasts with Shallow Measurements](https://mlsanity.com/paper/2610.10366/) (2026)

## Abstract (arXiv)

To address the high sampling cost of Diffusion Transformers (DiTs), feature caching offers a training-free acceleration method. However, existing methods rely on hand-crafted forecasting formulas that fail under aggressive skipping. We propose L2P (Learnable Linear Predictor), a simple data-driven caching framework that replaces fixed coefficients with learnable per-timestep weights. Rapidly trained in ~20 seconds on a single GPU, L2P accurately reconstructs current features from past trajectories. L2P significantly outperforms existing baselines: it achieves a 4.55x FLOPs reduction and 4.15x latency speedup on FLUX.1-dev, and maintains high visual fidelity under up to 7.18x acceleration on Qwen-Image models, where prior methods show noticeable quality degradation. Our results show learning linear predictors is highly effective for efficient DiT inference. Code is available at https://github.com/Aredstone/L2P-Cache.