constraint-based generator

Technique

A constraint-based generator models generation as a constraint satisfaction problem and samples outputs from the set of assignments satisfying the constraints. In CSP solution generation, a volume-weighted uniform spawning step combined with rejection of non-solutions can yield a uniform distribution over valid solutions.

First seen 6/18/2026

Last seen 6/18/2026

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Overview

A constraint-based generator is a generation technique that represents valid outputs as solutions to a set of constraints. In the procedural-content-generation setting, modeling generation as a constraint satisfaction problem supports both local and global constraints on generated outputs. Recent work on YORO pre-rolling describes this as a way to retain solver-based enforcement of global constraints while also shaping output statistics in WFC-like generators.

Constraint-based sampling pattern

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RELATIONSHIPS

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constraint-based sampling implements → 1e

The constraint-based generator implements constraint-based sampling by selecting elements and spawning points within them.

rejection sampling uses → 1e

The constraint-based generator uses rejection sampling to discard points that do not satisfy the constraints.

uniform sampling uses → 1e

The constraint-based generator uses uniform sampling by spawning points uniformly within each element.

solution uniformity evaluates → 1e

The constraint-based generator is proven to achieve solution uniformity, as the probability of sampling any particular solution is constant.

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constraint-based sampling IMPLEMENTS Extracted graph relationship

rejection sampling USES Extracted graph relationship

uniform sampling USES Extracted graph relationship

solution uniformity EVALUATES Extracted graph relationship

CITATIONS

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[1] Constraint-based generation can model procedural-content-generation tasks as constraint satisfaction problems with local and global constraints, and YORO pre-rolling targets statistical control in solver-based WFC-like constraint-based generators. You-Only-Randomize-Once: Shaping Statistical Properties in Constraint-based PCG

[2] In the CSP solution generator, spawn(e) is assumed to sample uniformly within an element e, with P(i | e) = 1 / v(e). An Efficient and Uniform CSP Solution Generator Generator

[3] The sampler selects an element with probability proportional to its volume and then spawns uniformly inside it, making the joint point-spawning probability constant over the considered elements. An Efficient and Uniform CSP Solution Generator Generator

[4] Samples from elements guaranteed to satisfy the constraints are always accepted, while samples from other elements are accepted only if they belong to the solution set; otherwise sampling repeats. An Efficient and Uniform CSP Solution Generator Generator

[5] The probability of returning any particular valid solution is constant across all solutions, proving uniformity of the returned CSP solution. An Efficient and Uniform CSP Solution Generator Generator