# VarDiU: A Variational Diffusive Upper Bound for One-Step Diffusion Distillation

arXiv: https://arxiv.org/abs/2508.20646 · HTML: https://mlsanity.com/paper/2508.20646/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 47 of its 59 references that are in the map.
- First posted on arXiv 28 Aug 2025.

## Placed in

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

## Builds on (most cited first, 30 of 47)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [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)
- [ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation](https://mlsanity.com/paper/2305.16213/) (2023)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Models](https://mlsanity.com/paper/2305.18455/) (2023)
- [Score identity Distillation: Exponentially Fast Distillation of Pretrained Diffusion Models for One-Step Generation](https://mlsanity.com/paper/2404.04057/) (2024)
- [Flow Annealed Importance Sampling Bootstrap](https://mlsanity.com/paper/2208.01893/) (2022)
- [TRACT: Denoising Diffusion Models with Transitive Closure Time-Distillation](https://mlsanity.com/paper/2303.04248/) (2023)

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

- [Diffusion Alignment Beyond KL: Variance Minimisation as Effective Policy Optimiser](https://mlsanity.com/paper/2602.12229/) (2026)

## Abstract (arXiv)

Recently, diffusion distillation methods have compressed thousand-step teacher diffusion models into one-step student generators while preserving sample quality. Most existing approaches train the student model using a diffusive divergence whose gradient is approximated via the student's score function, learned through denoising score matching (DSM). Since DSM training is imperfect, the resulting gradient estimate is inevitably biased, leading to sub-optimal performance. In this paper, we propose VarDiU (pronounced /va:rdju:/), a Variational Diffusive Upper Bound that admits an unbiased gradient estimator and can be directly applied to diffusion distillation. Using this objective, we compare our method with Diff-Instruct and demonstrate that it achieves higher generation quality and enables a more efficient and stable training procedure for one-step diffusion distillation.