Direct Preference Optimisation (DPO)  is effective at significantly improving the performance of large language models (LLMs)  on downstream tasks such as reasoning, summarisation, and alignment. Using pairs of preferred and dispreferred data, DPO models therelativeprobability of picking one response over another. In this work, first we show theoretically that the standard DPO loss can lead to areductionof the model’s likelihood of the preferred examples, as long as the relative probability between the preferred and dispreferred classes increases. We then show empirically that this phenomenon occurs when fine-tuning LLMs on common datasets, especially datasets in which the edit distance between pairs of completions is low. Using these insights, we design DPO-Positive (DPOP) , a new loss function and training procedure which avoids this failure mode. Surprisingly, we also find that DPOP significantly outperforms DPO across a wide variety of datasets and downstream tasks, including datasets with high edit distances between completions. By fine-tuning with DPOP, we create and release Smaug-34B and Smaug-72B, which achieve state-of-the-art open-source performance. Notably, Smaug-72B is nearly 2% better than any other open-source model on the HuggingFace Open LLM Leaderboard and becomes the first open-source LLM to surpass an average accuracy of 80%.