There has been immense progress recently in the visual quality of Stable Diffusion-based Super Resolution (SD-SR). However, deploying large diffusion models on computationally restricted devices such as mobile phones remains impractical due to the large model size and high latency. This is compounded for SR as it often operates at high res (e.g. 4Kx3K). In this work, we introduce Edge-SD-SR, the first parameter efficient and low latency diffusion model for image super-resolution. Edge-SD-SR consists of ~169M parameters, including UNet, encoder and decoder, and has a complexity of only ~142 GFLOPs. To maintain a high visual quality on such low compute budget, we introduce a number of training strategies: (i) A novel conditioning mechanism on the low resolution input, coined bidirectional conditioning, which tailors the SD model for the SR task. (ii) Joint training of the UNet and encoder, while decoupling the encodings of the HR and LR images and using a dedicated schedule. (iii) Finetuning the decoder using the UNet's output to directly tailor the decoder to the latents obtained at inference time. Edge-SD-SR runs efficiently on device, e.g. it can upscale a 128x128 patch to 512x512 in 38 msec while running on a Samsung S24 DSP, and of a 512x512 to 2048x2048 (requiring 25 model evaluations) in just ~1.1 sec. Furthermore, we show that Edge-SD-SR matches or even outperforms state-of-the-art SR approaches on the most established SR benchmarks.