# DCTdiff: Intriguing Properties of Image Generative Modeling in the DCT Space

arXiv: https://arxiv.org/abs/2412.15032 · HTML: https://mlsanity.com/paper/2412.15032/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 59 of its 79 references that are in the map.
- First posted on arXiv 19 Dec 2024.

## Placed in

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

## Builds on (most cited first, 30 of 59)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [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)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [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)
- [Magic3D: High-Resolution Text-to-3D Content Creation](https://mlsanity.com/paper/2211.10440/) (2022)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Two-Stream Convolutional Networks for Action Recognition in Videos](https://mlsanity.com/paper/1406.2199/) (2014)
- [Visual Autoregressive Modeling: Scalable Image Generation via Next-Scale Prediction](https://mlsanity.com/paper/2404.02905/) (2024)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)

## Built on by (most cited first, 30 of 34)

- [Improving the Diffusability of Autoencoders](https://mlsanity.com/paper/2502.14831/) (2025)
- [GestureLSM: Latent Shortcut based Co-Speech Gesture Generation with Spatial-Temporal Modeling](https://mlsanity.com/paper/2501.18898/) (2025)
- [The Prism Hypothesis: Harmonizing Semantic and Pixel Representations via Unified Autoencoding](https://mlsanity.com/paper/2512.19693/) (2025)
- [Semantics Lead the Way: Harmonizing Semantic and Texture Modeling with Asynchronous Latent Diffusion](https://mlsanity.com/paper/2512.04926/) (2025)
- [SemGes: Semantics-aware Co-Speech Gesture Generation using Semantic Coherence and Relevance Learning](https://mlsanity.com/paper/2507.19359/) (2025)
- [Contextual Gesture: Co-Speech Gesture Video Generation through Context-aware Gesture Representation](https://mlsanity.com/paper/2502.07239/) (2025)
- [Unleashing the Potential of Diffusion Models for End-to-End Autonomous Driving](https://mlsanity.com/paper/2602.22801/) (2026)
- [FreqPolicy: Frequency Autoregressive Visuomotor Policy with Continuous Tokens](https://mlsanity.com/paper/2506.01583/) (2025)
- [POLARIS: Projection-Orthogonal Least Squares for Robust and Adaptive Inversion in Diffusion Models](https://mlsanity.com/paper/2512.00369/) (2025)
- [Spectrum Matching: a Unified Perspective for Superior Diffusability in Latent Diffusion](https://mlsanity.com/paper/2603.14645/) (2026)
- [Improving Progressive Generation with Decomposable Flow Matching](https://mlsanity.com/paper/2506.19839/) (2025)
- [Free-T2M: Robust Text-to-Motion Generation for Humanoid Robots via Frequency-Domain](https://mlsanity.com/paper/2501.18232/) (2025)
- [Decoupled Residual Denoising Diffusion Models for Unified and Data Efficient Image-to-Image Translation](https://mlsanity.com/paper/2606.01048/) (2026)
- [ECHO: Edge-Cloud Humanoid Orchestration for Language-to-Motion Control](https://mlsanity.com/paper/2603.16188/) (2026)
- [SemConFlow: Semantic Grounding of Holistic Co-Speech Gesture Generation with Contrastive Flow-Matching](https://mlsanity.com/paper/2603.26553/) (2026)
- [WaveletDiff: Multilevel Wavelet Diffusion For Time Series Generation](https://mlsanity.com/paper/2510.11839/) (2025)
- [MemoGen: Can Past Experience Improve Future Text-to-Image Generation?](https://mlsanity.com/paper/2606.03243/) (2026)
- [WaiT for the Signal: Simple Frequency-Aware Flow-Matching](https://mlsanity.com/paper/2607.28760/) (2026)
- [Oracle Noise: Faster Semantic Spherical Alignment for Interpretable Latent Optimization](https://mlsanity.com/paper/2604.23540/) (2026)
- [Functional MRI Time Series Generation via Wavelet-Based Image Transform and Spectral Flow Matching for Brain Disorder Identification](https://mlsanity.com/paper/2605.30387/) (2026)
- [Show the Signal, Hide the Noise: Spectral Forcing for Pixel-Space Diffusion](https://mlsanity.com/paper/2606.15236/) (2026)
- [The Mechanics of CNN Filtering with Rectification](https://mlsanity.com/paper/2512.24338/) (2025)
- [Z2-Sampling: Zero-Cost Zigzag Trajectories for Semantic Alignment in Diffusion Models](https://mlsanity.com/paper/2604.23536/) (2026)
- [Everything at Every Scale: Scale-Invariant Diffusion with Continuous Super-Resolution](https://mlsanity.com/paper/2605.26032/) (2026)
- [HyFAD: Hybrid Time-Frequency Diffusion with Frequency-Aware Embedding for Time Series Imputation](https://mlsanity.com/paper/2606.05239/) (2026)
- [Cyclostationary Phase Conditioning for Medical Time Series Diffusion](https://mlsanity.com/paper/2609.34965/) (2026)
- [Dynamic Frequency Modulation for Controllable Text-driven Image Generation](https://mlsanity.com/paper/2602.10662/) (2026)
- [Structured State-Space Regularization for Generation-Friendly Image Tokenization](https://mlsanity.com/paper/2604.11089/) (2026)
- [DiffATS: Diffusion in Aligned Tensor Space](https://mlsanity.com/paper/2605.09275/) (2026)
- [Before the Body Moves: Learning Anticipatory Joint Intent for Language-Conditioned Humanoid Control](https://mlsanity.com/paper/2605.14417/) (2026)

## Abstract (arXiv)

This paper explores image modeling from the frequency space and introduces DCTdiff, an end-to-end diffusion generative paradigm that efficiently models images in the discrete cosine transform (DCT) space. We investigate the design space of DCTdiff and reveal the key design factors. Experiments on different frameworks (UViT, DiT), generation tasks, and various diffusion samplers demonstrate that DCTdiff outperforms pixel-based diffusion models regarding generative quality and training efficiency. Remarkably, DCTdiff can seamlessly scale up to 512×512 resolution without using the latent diffusion paradigm and beats latent diffusion (using SD-VAE) with only 1/4 training cost. Finally, we illustrate several intriguing properties of DCT image modeling. For example, we provide a theoretical proof of why 'image diffusion can be seen as spectral autoregression', bridging the gap between diffusion and autoregressive models. The effectiveness of DCTdiff and the introduced properties suggest a promising direction for image modeling in the frequency space. The code is https://github.com/forever208/DCTdiff.