☆ Save Sampling-based Inference — Why Probabilistic Token Selection Matters in LLM Decoding

09/13/2026

Sampling-based Inference is a decoding strategy that determines how an LLM chooses the next token during inference. When a language model receives a prompt, it does not immediately settle on a single next token. Instead, it scores many possible candidates and converts those scores into a probability distribution. Rather than always taking the most likely token, sampling draws from that distribution. As a result, the same prompt can follow different generation paths and produce different outputs.

Put simply: imagine that the next-token candidates are A·B·and C, and that A has the highest probability. A deterministic strategy that always chooses the top candidate would select A every time. Sampling still makes A the most likely choice, but B and C retain some chance of being selected. The choice is therefore random in a controlled sense: it follows probabilities computed by the model rather than treating all candidates equally.

Selecting the next token from a probability distribution

How It Works

• Turning logits into a probability distribution

  • Before the model can sample a token, it needs a way to compare the available next-token candidates. An autoregressive language model uses the tokens generated so far to compute a logit for every possible next token.
  • Logits are not probabilities. They are raw model scores that express the relative preference for one token over another.
  • Applying Softmax converts those logits into a probability distribution, giving each candidate a probability of being selected.
  • That distribution becomes the basis for sampling, forming a direct path from model scores to probabilistic token selection.

• Selecting a token from the probability distribution

  • At each generation step, Sampling-based Inference draws one token from the probability distribution produced by the model.
  • Higher-probability tokens are more likely to be selected, but the most likely token is not guaranteed to be chosen every time.
  • The selected token is then added to the context for the next step, which changes both the available candidates and their probabilities.
  • Because this process repeats autoregressively, choosing a different token early in the sequence can lead the rest of the output in a completely different direction.

• How sampling differs from Greedy Decoding

  • The purpose of sampling becomes clearer when compared with Greedy Decoding. Greedy Decoding always chooses the highest-probability token at each step.
  • Sampling-based Inference does not lock generation to the top candidate. Instead, it chooses among candidates according to their probabilities.
  • This makes Greedy Decoding more predictable, but it can also reduce the range of expressions the model produces.
  • Sampling keeps multiple candidates in play, increasing output diversity while potentially reducing consistency.

• Controlling the distribution with temperature

  • Even when sampling is enabled, we may want to control how strongly the model favors tokens with higher logits. Temperature does this by reshaping the probability distribution before a token is selected.

  • $$ P_i = \frac{\exp(z_i / T)}{\sum_j \exp(z_j / T)} $$

    zi is the logit for token i, T is the temperature, and Pi is the probability of selecting token i during sampling.

  • Suppose two tokens have logits of 2 and 1. With a temperature of 1, their selection probabilities are approximately 0.73 and 0.27. Lowering the temperature to 0.5 sharpens the distribution, producing probabilities of roughly 0.88 and 0.12 and placing more weight on the token with the higher logit.

  • Raising the temperature to 2 has the opposite effect. The probabilities become approximately 0.62 and 0.38, making the two candidates more similar in likelihood. Lower temperatures therefore make token selection more concentrated and predictable, while higher temperatures give more candidates a meaningful chance of being selected. This changes inference behavior without modifying the model’s weights.

• Balancing diversity and stability

  • Once temperature is introduced, sampling becomes a practical trade-off between output diversity and stability.
  • When varied expression is desirable, the decoding configuration can preserve meaningful probabilities across several candidate tokens.
  • When consistency and accuracy matter more, a more restrictive sampling configuration may be preferable.
  • Sampling is therefore not inherently better than deterministic decoding. It is a decoding strategy that can be tuned to produce the kind of output behavior a given application requires.

Significance and Limitations

A major advantage of Sampling-based Inference is that it lets an LLM’s output behavior be adjusted at inference time without retraining the model. By changing how tokens are selected from the model’s probability distribution, a system can avoid being limited to a single deterministic generation path and produce a broader range of outputs. In practical LLM applications, decoding settings therefore provide an important way to control output diversity and overall generation behavior.

The same probabilistic selection process also introduces variability. If the sampling configuration is too permissive, the model may produce unexpected or lower-quality outputs, making consistent behavior harder to maintain. Real-world systems therefore need to choose decoding settings according to the desired output characteristics and balance diversity against stability as a practical trade-off.

Recommended prerequisite reading (3/5)

+2

• Sample Generation — How LLMs Select Tokens from a Probability Distribution
• Token Sampling — Why Preserving the Probability Distribution Produces More Natural Generation
• SMLD (Score Matching with Langevin Dynamics) — Score-Based Sampling

• NADE (Neural Autoregressive Distribution Estimator) — How Generative Models Learn Probability Distributions
• Flow-based Models — Learning Data Distributions Through Invertible Transformations

Recommended next reading (5/15)

+5

• Stochastic Decoding — Why Probabilistic Choices Create Diversity in Language Generation
• Greedy Decoding — Why the Best Next Token May Not Produce the Best Sequence
• Top-p Sampling (Nucleus Sampling) — Why the Number of Candidates Changes Dynamically
• Latent Variable Inference — Inferring Hidden Structure from Observed Data
• Likelihood-Free Modeling — Inferring Generative Processes with Simulation-Based Inference

• Degradation Model — A Probabilistic Model That Defines the Data Corruption Process
• Likelihood-Based Modeling — Learning Data Distributions with Maximum Likelihood
• Conditional Generation — How Generative Models Control Their Outputs
• Model Distribution — How LLMs Learn Output Probabilities
• Latent Variable Models — Modeling the Relationship Between Observed and Hidden Variables

• PixelCNN — How Autoregressive Image Generation Learns Pixel Probabilities
• Distribution Matching — How Generative Models Learn Real-World Data Distributions
• Density Modeling — How Probability Density Is Estimated from Image Vectors
• Data Distribution vs Model Distribution — How Generative Models Approximate Real-World Data
• Conditional Density Modeling — Learning Data Distributions Under Specific Conditions

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Related concepts (8/9)

+1

• Probability Normalization — How Softmax Converts Model Outputs into a Probability Distribution
• Probability Distribution Comparison — How to Measure and Interpret Differences Between Distributions
• Unnormalized Probability Models — Why Models Use Scores Before Normalization
• Multinoulli Distribution — Modeling One Choice Among Many Categories
• Valid Probability Distributions: Why Probabilities Must Sum to 1
• Markov Chain — How Transition Probabilities Drive State Evolution
• Normalizing Constant — The Key to Turning Relative Scores into a Probability Distribution
• Stochastic Inference — Reasoning with Uncertainty in AI

• Stationary Distribution — How Long-Run Probabilities Emerge in a Markov Chain

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🔖 Tags: greedy decoding · LLM Decoding · Probability Distribution · Sampling-based Inference · temperature · token sampling