Recent studies (Doshi & Hauser 2024, Bisbee et al. 2024, Xie et al. 2026) have highlighted that large language models (LLMs) often produce under‑diverse outputs, a phenomenon known as mode collapse: different responses tend to be overly similar or even identical, falling short of the diversity observed in the target population. This work shows that whether mode collapse—or its opposite, over‑dispersion—occurs depends on the specific model and dataset.
With enough supervised fine‑tuning (SFT) data, the output diversity of an LLM converges toward that of the target distribution from which the fine‑tuning data are drawn. To quantify this convergence we use two metrics:
- Collision probability – the probability that two independently sampled responses to the same fixed prompt are identical;
- Kernel similarity – the expected similarity of two sampled responses under a chosen kernel function.
We derive a bias‑variance decomposition of the expected gap between the model’s and the target’s collision probabilities, demonstrating that SFT is not inherently biased toward either mode collapse or over‑dispersion. Finite‑sample SFT can leave a model under‑ or over‑dispersed depending on the model architecture and data characteristics.
Moreover, we prove that the absolute gap is bounded by the square root of the KL divergence from the target distribution to the model: $$ |P{model}(\text{collision}) - P{target}(\text{collision})| \le \sqrt{D{KL}(P{target}|P_{model})} $$ Consequently, a model that is sufficiently close to optimal under population cross‑entropy cannot exhibit arbitrarily miscalibrated diversity.
We validate the decomposition and the bound in three experimental settings:
- Small transformers trained on synthetic languages;
- Four LLMs fine‑tuned on human survey data;
- The same LLMs fine‑tuned on CodeNet, a dataset of human code solutions. In all cases, increasing the amount of target data moves model diversity toward the human (or synthetic) level, matching our theoretical predictions. The results indicate that diversity miscalibration stems from finite‑sample error and shrinks as SFT better approximates the target distribution.
Review: The paper offers a probabilistic framework for understanding and correcting LLM diversity issues, and empirically confirms that supervised fine‑tuning can effectively mitigate mode collapse, providing practical guidance for building more reliable generative models.