Direct Preference Optimization (DPO) has been proposed as a promising alternative to Proximal Policy Optimization (PPO) based Reinforcement Learning with Human Feedback (RLHF). However, empirical evaluations consistently reveal suboptimal performance in DPO compared to common RLHF pipelines. In this work, we conduct a systematic analysis of DPO's training dynamics and identify gradient imbalance as a critical limitation. We demonstrate theoretically and empirically that this imbalance perturbs optimization trajectories, destabilizes learning, and induces suboptimal convergence. To address this issue, we propose Balanced-DPO, a simple yet effective modification to the DPO objective that introduces a computationally efficient gradient reweighting mechanism. Our experiments demonstrate the effectiveness of Balanced-DPO, validating the theoretical findings and confirming that addressing gradient imbalance is key to improving DPO's performance, highlighting a promising direction for future research.

Langevin diffusion is a commonly used tool for sampling from a given distribution. In this work, we establish that when the target density $p^*$ is such that $\log p^*$ is $L$ smooth and $m$ strongly convex, discrete Langevin diffusion produces a distribution $p$ with $KL(p||p^*)\leq \epsilon$ in $\tilde{O}(\frac{d}{\epsilon})$ steps, where $d$ is the dimension of the sample space. We also study the convergence rate when the strong-convexity assumption is absent. By considering the Langevin diffusion as a gradient flow in the space of probability distributions, we obtain an elegant analysis that applies to the stronger property of convergence in KL-divergence and gives a conceptually simpler proof of the best-known convergence results in weaker metrics.