In ultrasound imaging the appearance of homogeneous regions of tissue is subject to speckle, which for certain applications can make the detection of tissue irregularities difficult. To cope with this, it is common practice to apply speckle reduction filters to the images. Most conventional filtering techniques are fairly hand-crafted and often need to be finely tuned to the present hardware, imaging scheme and application. Learning based techniques on the other hand suffer from the need for a target image for training (in case of fully supervised techniques) or require narrow, complex physics-based models of the speckle appearance that might not apply in all cases. With this work we propose a deep-learning based method for speckle removal without these limitations. To enable this, we make use of realistic ultrasound simulation techniques that allow for instantiation of several independent speckle realizations that represent the exact same tissue, thus allowing for the application of image reconstruction techniques that work with pairs of differently corrupted data. Compared to two other state-of-the-art approaches (non-local means and the Optimized Bayesian non-local means filter) our method performs favorably in qualitative comparisons and quantitative evaluation, despite being trained on simulations alone, and is several orders of magnitude faster.