Pair each decoding strategy with its determinism and diversity profile.

At each decode step the model produces a probability distribution over its entire vocabulary. The decoding strategy is what turns that distribution into a single chosen token. **Greedy decoding** picks the highest-probability token (the argmax) every time. The same prompt always produces the same output. It is the fastest strategy and works well when you want consistency, but it can produce repetitive, robotic text on creative tasks. **Temperature sampling** draws a token at random from the distribution. The temperature parameter scales the logits before softmax: lower temperature concentrates mass on the most likely tokens, higher temperature flattens it. Setting temperature to exactly zero collapses to greedy, because dividing by zero pushes all mass onto the argmax. Sampling is usually combined with top-k or top-p (nucleus) filters that throw away the long tail of low-probability tokens before sampling, preventing rare-token derailments. **Beam search** keeps several candidate sequences alive at once (typically 3 to 8) and extends each step by step. At the end it picks the sequence with the highest overall probability. It is more globally optimal than greedy but much slower, and rarely used for chat-style LLM serving.

Decoding strategies all start from the same place: the model's post-softmax distribution over the vocabulary at each step. They differ in how they collapse that distribution into a single chosen token. **Greedy decoding** takes the argmax. It is deterministic, fastest (no sampling overhead), and tends to produce repetitive output because the most likely token is often a function word that pulls the model into common phrases. Used for tasks where consistency matters: code completion, structured output, eval reproducibility. **Temperature sampling** divides logits by a temperature T before softmax. Lower T sharpens the distribution; higher T flattens it. With T=1 you sample from the model's native distribution. Combine with top-p (nucleus): renormalise over the smallest set of tokens whose cumulative probability exceeds p, typically 0.9 to 0.95. Or top-k: keep only the k highest-probability tokens, typically 40 to 50. Both filters cut the rare-token tail before the sampler can pick from it. Setting temperature to 0 collapses to greedy mathematically: logits divided by zero diverge, and softmax of diverging logits with a unique maximum places all mass on that single token. Production APIs implement this as a special case rather than literally dividing by zero. **Beam search** maintains a beam of B candidate sequences. Each step expands every candidate by every plausible next token, scores the resulting B times V sequences, and keeps the top B. It is more globally optimal than greedy but costs B times the compute and produces less natural output for open-ended generation, so it has fallen out of favour for chat LLMs.