Image-to-Image (I2I) translation involves converting an im- age from one domain to another. Deterministic I2I transla- tion, such as in image super-resolution, extends this con- cept 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 denois- ing 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 pro- cess) to produce faithful output with negligible variance and high image quality in I2I translations. Our extensive exper- iments on benchmark datasets including image generation and super-resolution demonstrate the consistent and supe- rior performance of Dual-approx Bridge in terms of im- age quality and faithfulness to GT when compared to both stochastic and deterministic baselines. Project page and code: https://github.com/bohan95/dual-app-bridge