# Solving Diffusion ODEs with Optimal Boundary Conditions for Better Image Super-Resolution arXiv: https://arxiv.org/abs/2305.15357 ยท HTML: https://mlsanity.com/paper/2305.15357/ ## Key facts - Cited by 7 papers in the map (data through 14 Oct 2026). - Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. - Builds on 50 of its 58 references that are in the map. - First posted on arXiv 24 May 2023. ## Placed in - Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/) ## Builds on (most cited first, 30 of 50) - [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014) - [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) - [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021) - [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021) - [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) - [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) - [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022) - [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022) - [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022) - [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021) - [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021) - [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022) - [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022) - [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016) - [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021) - [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022) - [Make-A-Video: Text-to-Video Generation without Text-Video Data](https://mlsanity.com/paper/2209.14792/) (2022) - [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017) - [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018) - [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021) - [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021) - [Image Super-Resolution Using Very Deep Residual Channel Attention Networks](https://mlsanity.com/paper/1807.02758/) (2018) - [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018) - [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021) - [Real-ESRGAN: Training Real-World Blind Super-Resolution with Pure Synthetic Data](https://mlsanity.com/paper/2107.10833/) (2021) ## Built on by (most cited first, 7 of 7) - [Any-Size-Diffusion: Toward Efficient Text-Driven Synthesis for Any-Size HD Images](https://mlsanity.com/paper/2308.16582/) (2023) - [Diffusion Enhancement for Cloud Removal in Ultra-Resolution Remote Sensing Imagery](https://mlsanity.com/paper/2401.15105/) (2024) - [Correcting Diffusion-Based Perceptual Image Compression with Privileged End-to-End Decoder](https://mlsanity.com/paper/2404.04916/) (2024) - [Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators](https://mlsanity.com/paper/2512.23463/) (2025) - [TurboVSR: Fantastic Video Upscalers and Where to Find Them](https://mlsanity.com/paper/2506.23618/) (2025) - [Language-based Image Colorization: A Benchmark and Beyond](https://mlsanity.com/paper/2503.14974/) (2025) - [Deterministic Medical Image Translation via High-fidelity Brownian Bridges](https://mlsanity.com/paper/2503.22531/) (2025) ## Abstract (arXiv) Diffusion models, as a kind of powerful generative model, have given impressive results on image super-resolution (SR) tasks. However, due to the randomness introduced in the reverse process of diffusion models, the performances of diffusion-based SR models are fluctuating at every time of sampling, especially for samplers with few resampled steps. This inherent randomness of diffusion models results in ineffectiveness and instability, making it challenging for users to guarantee the quality of SR results. However, our work takes this randomness as an opportunity: fully analyzing and leveraging it leads to the construction of an effective plug-and-play sampling method that owns the potential to benefit a series of diffusion-based SR methods. More in detail, we propose to steadily sample high-quality SR images from pre-trained diffusion-based SR models by solving diffusion ordinary differential equations (diffusion ODEs) with optimal boundary conditions (BCs) and analyze the characteristics between the choices of BCs and their corresponding SR results. Our analysis shows the route to obtain an approximately optimal BC via an efficient exploration in the whole space. The quality of SR results sampled by the proposed method with fewer steps outperforms the quality of results sampled by current methods with randomness from the same pre-trained diffusion-based SR model, which means that our sampling method "boosts" current diffusion-based SR models without any additional training.