# iFSQ: Improving FSQ for Image Generation with 1 Line of Code

arXiv: https://arxiv.org/abs/2601.17124 · HTML: https://mlsanity.com/paper/2601.17124/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 36 of its 48 references that are in the map.
- First posted on arXiv 23 Jan 2026.

## Placed in

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

## Builds on (most cited first, 30 of 36)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [Cosmos World Foundation Model Platform for Physical AI](https://mlsanity.com/paper/2501.03575/) (2025)
- [Autoregressive Model Beats Diffusion: Llama for Scalable Image Generation](https://mlsanity.com/paper/2406.06525/) (2024)
- [Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think](https://mlsanity.com/paper/2410.06940/) (2024)
- [Language Model Beats Diffusion -- Tokenizer is Key to Visual Generation](https://mlsanity.com/paper/2310.05737/) (2023)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Jukebox: A Generative Model for Music](https://mlsanity.com/paper/2005.00341/) (2020)
- [Scaling up GANs for Text-to-Image Synthesis](https://mlsanity.com/paper/2303.05511/) (2023)
- [Finite Scalar Quantization: VQ-VAE Made Simple](https://mlsanity.com/paper/2309.15505/) (2023)
- [Reconstruction vs. Generation: Taming Optimization Dilemma in Latent Diffusion Models](https://mlsanity.com/paper/2501.01423/) (2025)
- [LLM-QAT: Data-Free Quantization Aware Training for Large Language Models](https://mlsanity.com/paper/2305.17888/) (2023)
- [CosyVoice 2: Scalable Streaming Speech Synthesis with Large Language Models](https://mlsanity.com/paper/2412.10117/) (2024)
- [Masked Autoencoders Are Effective Tokenizers for Diffusion Models](https://mlsanity.com/paper/2502.03444/) (2025)
- [Uniworld-V2: Reinforce Image Editing with Diffusion Negative-aware Finetuning and MLLM Implicit Feedback](https://mlsanity.com/paper/2510.16888/) (2025)
- [WF-VAE: Enhancing Video VAE by Wavelet-Driven Energy Flow for Latent Video Diffusion Model](https://mlsanity.com/paper/2411.17459/) (2024)
- [Scaling Transformers for Low-Bitrate High-Quality Speech Coding](https://mlsanity.com/paper/2411.19842/) (2024)
- [Vision as a Dialect: Unifying Visual Understanding and Generation via Text-Aligned Representations](https://mlsanity.com/paper/2506.18898/) (2025)
- [VideoWorld: Exploring Knowledge Learning from Unlabeled Videos](https://mlsanity.com/paper/2501.09781/) (2025)
- [VidTok: A Versatile and Open-Source Video Tokenizer](https://mlsanity.com/paper/2412.13061/) (2024)

## Built on by (most cited first, 4 of 4)

- [Heracles: Bridging Precise Tracking and Generative Synthesis for General Humanoid Control](https://mlsanity.com/paper/2603.27756/) (2026)
- [GEAR: Guided End-to-End AutoRegression for Image Synthesis](https://mlsanity.com/paper/2606.32039/) (2026)
- [Beyond Token-Level Cross-Entropy: Fr'echet Distributional Post-Training for Autoregressive Image Generation](https://mlsanity.com/paper/2608.00562/) (2026)
- [DashVMC: Real-Time Discrete World Model Control in Geometry Dash](https://mlsanity.com/paper/2609.40003/) (2026)

## Abstract (arXiv)

The field of image generation is currently bifurcated into autoregressive (AR) models operating on discrete tokens and diffusion models utilizing continuous latents. This divide, rooted in the distinction between VQ-VAEs and VAEs, hinders unified modeling and fair benchmarking. Finite Scalar Quantization (FSQ) offers a theoretical bridge, yet vanilla FSQ suffers from a critical flaw: its equal-interval quantization can cause activation collapse. This mismatch forces a trade-off between reconstruction fidelity and information efficiency. In this work, we resolve this dilemma by simply replacing the activation function in original FSQ with a distribution-matching mapping to enforce a uniform prior. Termed iFSQ, this simple strategy requires just one line of code yet mathematically guarantees both optimal bin utilization and reconstruction precision. Leveraging iFSQ as a controlled benchmark, we uncover two key insights: (1) The optimal equilibrium between discrete and continuous representations lies at approximately 4 bits per dimension. (2) Under identical reconstruction constraints, AR models exhibit rapid initial convergence, whereas diffusion models achieve a superior performance ceiling, suggesting that strict sequential ordering may limit the upper bounds of generation quality. Finally, we extend our analysis by adapting Representation Alignment (REPA) to AR models, yielding LlamaGen-REPA. Codes is available at https://github.com/Tencent-Hunyuan/iFSQ