# SimFlow: Simplified and End-to-End Training of Latent Normalizing Flows

arXiv: https://arxiv.org/abs/2512.04084 · HTML: https://mlsanity.com/paper/2512.04084/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 65 of its 74 references that are in the map.
- First posted on arXiv 3 Dec 2025.

## Builds on (most cited first, 30 of 65)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Visual Autoregressive Modeling: Scalable Image Generation via Next-Scale Prediction](https://mlsanity.com/paper/2404.02905/) (2024)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Autoregressive Model Beats Diffusion: Llama for Scalable Image Generation](https://mlsanity.com/paper/2406.06525/) (2024)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think](https://mlsanity.com/paper/2410.06940/) (2024)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Autoregressive Image Generation without Vector Quantization](https://mlsanity.com/paper/2406.11838/) (2024)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Language Model Beats Diffusion -- Tokenizer is Key to Visual Generation](https://mlsanity.com/paper/2310.05737/) (2023)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [All are Worth Words: A ViT Backbone for Diffusion Models](https://mlsanity.com/paper/2209.12152/) (2022)
- [StyleGAN-XL: Scaling StyleGAN to Large Diverse Datasets](https://mlsanity.com/paper/2202.00273/) (2022)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [Reconstruction vs. Generation: Taming Optimization Dilemma in Latent Diffusion Models](https://mlsanity.com/paper/2501.01423/) (2025)
- [Diffusion Transformers with Representation Autoencoders](https://mlsanity.com/paper/2510.11690/) (2025)
- [MDTv2: Masked Diffusion Transformer is a Strong Image Synthesizer](https://mlsanity.com/paper/2303.14389/) (2023)

## Built on by (most cited first, 7 of 7)

- [GenFirst: Generation Before Reconstruction for Stable End-to-End Latent Generative Modeling](https://mlsanity.com/paper/2608.29335/) (2026)
- [MIMFlow: Integrating Masked Image Modeling with Normalizing Flows for End-to-End Image Generation](https://mlsanity.com/paper/2606.26016/) (2026)
- [Rethinking Refinement: Correcting Generative Bias without Noise Injection](https://mlsanity.com/paper/2601.21182/) (2026)
- [SRC-Flow: Compact Semantic Representations Enable Normalizing Flows for Image Generation](https://mlsanity.com/paper/2605.18267/) (2026)
- [RoMAN-Flow: Taming Autoregressive Normalizing Flows for Offline Reinforcement Learning in Robotic Manipulation](https://mlsanity.com/paper/2608.20208/) (2026)
- [PixelDiT2: Representation-Grounded Pixel Diffusion Transformers](https://mlsanity.com/paper/2609.24919/) (2026)
- [Empirical Variational Autoencoder](https://mlsanity.com/paper/2610.06545/) (2026)

## Abstract (arXiv)

Normalizing Flows (NFs) learn invertible mappings between the data and a Gaussian distribution. Prior works usually suffer from two limitations. First, they add random noise to training samples or VAE latents as data augmentation, introducing complex pipelines including extra noising and denoising steps. Second, they use a pretrained and frozen VAE encoder, resulting in suboptimal reconstruction and generation quality. In this paper, we find that the two issues can be solved in a very simple way: just fixing the variance (which would otherwise be predicted by the VAE encoder) to a constant (e.g., 0.5). On the one hand, this method allows the encoder to output a broader distribution of tokens and the decoder to learn to reconstruct clean images from the augmented token distribution, avoiding additional noise or denoising design. On the other hand, fixed variance simplifies the VAE evidence lower bound, making it stable to train an NF with a VAE jointly. On the ImageNet 256 × 256 generation task, our model SimFlow obtains a gFID score of 2.15, outperforming the state-of-the-art method STARFlow (gFID 2.40). Moreover, SimFlow can be seamlessly integrated with the end-to-end representation alignment (REPA-E) method and achieves an improved gFID of 1.91, setting a new state of the art among NFs.