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Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators

Bohan Xiao, Peiyong Wang, Qisheng He, Ming Dong

TL;DR

This work tackles the need for deterministic, faithful image-to-image translation with high fidelity to ground truth. It introduces Dual-approx Bridge, a Brownian-bridge diffusion framework that uses two neural approximators—one in the forward process to estimate the initial state $X_0$ and one in the reverse process to estimate the noise increment—to produce a unique, high-quality output for each input. The method blends forward score estimation with a deterministic reverse path, achieving state-of-the-art fidelity (PSNR/SSIM) while maintaining image quality competitive with stochastic diffusion, and it does so with significantly fewer sampling steps than traditional diffusion approaches. Empirical results on Cityscapes, Edges2Handbags, and related benchmarks demonstrate superior faithfulness to ground truth and robust deterministic performance, underscoring the approach’s potential for applications where repeatability and precision are crucial. Future work includes integrating different SDE formulations to further enhance stability and quality.

Abstract

Image-to-Image (I2I) translation involves converting an image from one domain to another. Deterministic I2I translation, such as in image super-resolution, extends this concept by guaranteeing that each input generates a consistent and predictable output, closely matching the ground truth (GT) with high fidelity. In this paper, we propose a denoising Brownian bridge model with dual approximators (Dual-approx Bridge), a novel generative model that exploits the Brownian bridge dynamics and two neural network-based approximators (one for forward and one for reverse process) to produce faithful output with negligible variance and high image quality in I2I translations. Our extensive experiments on benchmark datasets including image generation and super-resolution demonstrate the consistent and superior performance of Dual-approx Bridge in terms of image quality and faithfulness to GT when compared to both stochastic and deterministic baselines. Project page and code: https://github.com/bohan95/dual-app-bridge

Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators

TL;DR

This work tackles the need for deterministic, faithful image-to-image translation with high fidelity to ground truth. It introduces Dual-approx Bridge, a Brownian-bridge diffusion framework that uses two neural approximators—one in the forward process to estimate the initial state and one in the reverse process to estimate the noise increment—to produce a unique, high-quality output for each input. The method blends forward score estimation with a deterministic reverse path, achieving state-of-the-art fidelity (PSNR/SSIM) while maintaining image quality competitive with stochastic diffusion, and it does so with significantly fewer sampling steps than traditional diffusion approaches. Empirical results on Cityscapes, Edges2Handbags, and related benchmarks demonstrate superior faithfulness to ground truth and robust deterministic performance, underscoring the approach’s potential for applications where repeatability and precision are crucial. Future work includes integrating different SDE formulations to further enhance stability and quality.

Abstract

Image-to-Image (I2I) translation involves converting an image from one domain to another. Deterministic I2I translation, such as in image super-resolution, extends this concept by guaranteeing that each input generates a consistent and predictable output, closely matching the ground truth (GT) with high fidelity. In this paper, we propose a denoising Brownian bridge model with dual approximators (Dual-approx Bridge), a novel generative model that exploits the Brownian bridge dynamics and two neural network-based approximators (one for forward and one for reverse process) to produce faithful output with negligible variance and high image quality in I2I translations. Our extensive experiments on benchmark datasets including image generation and super-resolution demonstrate the consistent and superior performance of Dual-approx Bridge in terms of image quality and faithfulness to GT when compared to both stochastic and deterministic baselines. Project page and code: https://github.com/bohan95/dual-app-bridge
Paper Structure (18 sections, 18 equations, 8 figures, 6 tables, 3 algorithms)

This paper contains 18 sections, 18 equations, 8 figures, 6 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Image-to-Image Translation
  4. Brown Bridge
  5. Generative Adversarial Networks
  6. Diffusion and Bridge Models
  7. Deterministic Dual-approx Bridge
  8. Score-Based SDE
  9. Training of Neural Network Approximators
  10. Sampling
  11. Algorithm
  12. Experiments
  13. Ablation Study
  14. Impact of Sampling Steps
  15. Faithfulness Evaluation
  16. ...and 3 more sections

Figures (8)

  • Figure 1: Sampling comparison between SDE-based sampler, PF-ODE-based sampler, and Dual-approx Bridge. The circular area within the dashed circle indicates where the SDE-based sampling outputs land. (a) SDE-based Sampling: diverse outputs of high image quality. (b) PF-ODE-based Sampling: deterministic outputs lack of fine details of ground truth (GT). (c) Dual-approx Bridge Sampling: deterministic output with fine details of GT.
  • Figure 2: Training process of the two approximators (top-left: forward diffusive process, bottom-left: reverse diffusive process). Right: Sampling workflow with both approximators in action.
  • Figure 3: Qualitative comparison with Brownian bridges using SDE-based and PF-ODE-based samplers on Edges2Handbags. Three sampling trials are conducted by each model given the same input. Standard deviation among sampling results by our model, SDE-based and PF-ODE-based sampler are 0.0001, 0.1030 and 0, respectively.
  • Figure 4: Qualitative comparison between Dual-approx Bridge and SOTA methods on the Cityscapes dataset.
  • Figure 5: Qualitative comparison on BSD100 datasets.
  • ...and 3 more figures