The catch: parallel commits are independent commits

There is a price for committing several tokens in one pass, and it is worth naming precisely because the maths section will formalize it. Within a single pass, the model produces a separate distribution for each blank, and sampling them simultaneously treats them as independent. Suppose two adjacent blanks should be either “hot dog” or “ice cream”, each with probability ½. Independent sampling happily produces “hot cream” a quarter of the time. Committing fewer tokens per pass (more passes) shrinks this coupling error; committing more (fewer passes) grows it. The step count is exactly the dial that trades speed against coordination.

Don’t take the 25% on faith — run the experiment. Draw samples in both modes and watch the tallies converge:

Predict first — in one-pass mode, what fraction will be coherent?

no samples yet

Target: “hot dog” or “ice cream”, 50/50. Each word’s marginal is a fair coin flip, so the one-pass mode settles near 50% coherent (¼ “hot cream” + ¼ “ice dog”), while spending a second pass conditions the second word on the first and never errs. Speed bought with coordination, measured.

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