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Dilated and transposed convolutions are widely used in modern convolutional neural networks (CNNs). These kernels are used extensively during CNN training and inference of applications such as image segmentation and high-resolution image generation. Although these kernels have grown in popularity, they stress current compute systems due to their high memory intensity, exascale compute demands, and large energy consumption. We find that commonly-used low-power CNN inference accelerators based on spatial architectures are not optimized for both of these convolutional kernels. Dilated and transposed convolutions introduce significant zero padding when mapped to the underlying spatial architecture, significantly degrading performance and energy efficiency. Existing approaches that address this issue require significant design changes to the otherwise simple, efficient, and well-adopted architectures used to compute direct convolutions. To address this challenge, we propose EcoFlow, a new set of dataflows and mapping algorithms for dilated and transposed convolutions. These algorithms are tailored to execute efficiently on existing low-cost, small-scale spatial architectures and requires minimal changes to the network-on-chip of existing accelerators. EcoFlow eliminates zero padding through careful dataflow orchestration and data mapping tailored to the spatial architecture. EcoFlow enables flexible and high-performance transpose and dilated convolutions on architectures that are otherwise optimized for CNN inference. We evaluate the efficiency of EcoFlow on CNN training workloads and Generative Adversarial Network (GAN) training workloads. Experiments in our new cycle-accurate simulator show that EcoFlow 1) reduces end-to-end CNN training time between 7-85%, and 2) improves end-to-end GAN training performance between 29-42%, compared to state-of-the-art CNN inference accelerators.