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The biomedical field offers many learning tasks that share unique challenges: large amounts of unpaired data, and a high cost to generate labels. In this work, we develop a method to address these issues with semi-supervised learning in regression tasks (e.g., translation from source to target). Our model uses adversarial signals to learn from unpaired datapoints, and imposes a cycle-loss reconstruction error penalty to regularize mappings in either direction against one another. We first evaluate our method on synthetic experiments, demonstrating two primary advantages of the system: 1) distribution matching via the adversarial loss and 2) regularization towards invertible mappings via the cycle loss. We then show a regularization effect and improved performance when paired data is supplemented by additional unpaired data on two real biomedical regression tasks: estimating the physiological effect of medical treatments, and extrapolating gene expression (transcriptomics) signals. Our proposed technique is a promising initial step towards more robust use of adversarial signals in semi-supervised regression, and could be useful for other tasks (e.g., causal inference or modality translation) in the biomedical field.