diff --git a/src/Type/Constant/ConstantArrayType.php b/src/Type/Constant/ConstantArrayType.php
index 8850f7f45a..2077f69256 100644
--- a/src/Type/Constant/ConstantArrayType.php
+++ b/src/Type/Constant/ConstantArrayType.php
@@ -969,9 +969,9 @@ public function fillKeysArray(Type $valueType): Type
 					return $stringKeyType;
 				}
 
-				$builder->setOffsetValueType($stringKeyType, $valueType, $this->isOptionalKey($i));
+				$builder->setOffsetValueType($stringKeyType, $valueType, $this->isOptionalKey($i) || count($stringKeyType->getConstantScalarTypes()) > 1);
 			} else {
-				$builder->setOffsetValueType($keyType, $valueType, $this->isOptionalKey($i));
+				$builder->setOffsetValueType($keyType, $valueType, $this->isOptionalKey($i) || count($keyType->getConstantScalarTypes()) > 1);
 			}
 		}
 
@@ -984,10 +984,11 @@ public function flipArray(): Type
 
 		foreach ($this->keyTypes as $i => $keyType) {
 			$valueType = $this->valueTypes[$i];
+			$offsetType = $valueType->toArrayKey();
 			$builder->setOffsetValueType(
-				$valueType->toArrayKey(),
+				$offsetType,
 				$keyType,
-				$this->isOptionalKey($i),
+				$this->isOptionalKey($i) || count($offsetType->getConstantScalarTypes()) > 1,
 			);
 		}
 
diff --git a/src/Type/Php/ArrayFillKeysFunctionReturnTypeExtension.php b/src/Type/Php/ArrayFillKeysFunctionReturnTypeExtension.php
index c961c45362..7a9474f5c6 100644
--- a/src/Type/Php/ArrayFillKeysFunctionReturnTypeExtension.php
+++ b/src/Type/Php/ArrayFillKeysFunctionReturnTypeExtension.php
@@ -7,10 +7,12 @@
 use PHPStan\DependencyInjection\AutowiredService;
 use PHPStan\Php\PhpVersion;
 use PHPStan\Reflection\FunctionReflection;
+use PHPStan\Type\Accessory\NonEmptyArrayType;
 use PHPStan\Type\DynamicFunctionReturnTypeExtension;
 use PHPStan\Type\NeverType;
 use PHPStan\Type\NullType;
 use PHPStan\Type\Type;
+use PHPStan\Type\TypeCombinator;
 use function count;
 
 #[AutowiredService]
@@ -38,7 +40,11 @@ public function getTypeFromFunctionCall(FunctionReflection $functionReflection,
 			return $this->phpVersion->arrayFunctionsReturnNullWithNonArray() ? new NullType() : new NeverType();
 		}
 
-		return $keysType->fillKeysArray($scope->getType($args[1]->value));
+		$filled = $keysType->fillKeysArray($scope->getType($args[1]->value));
+		if ($keysType->isIterableAtLeastOnce()->yes() && $filled->isArray()->yes()) {
+			return TypeCombinator::intersect($filled, new NonEmptyArrayType());
+		}
+		return $filled;
 	}
 
 }
diff --git a/tests/PHPStan/Analyser/nsrt/bug-14656.php b/tests/PHPStan/Analyser/nsrt/bug-14656.php
new file mode 100644
index 0000000000..85c422c558
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-14656.php
@@ -0,0 +1,47 @@
+<?php declare(strict_types = 1);
+
+namespace Bug14656;
+
+use function PHPStan\Testing\assertType;
+
+class ArrayFlipUnionValues
+{
+	/** @param array{0: 'a'|'b'|'c', 1: 'a'|'b'|'c', 2: 'a'|'b'|'c'} $a */
+	public function allUnion(array $a): void
+	{
+		assertType("non-empty-array{a?: 0|1|2, b?: 0|1|2, c?: 0|1|2}", array_flip($a));
+	}
+
+	/** @param array{0: 'a'|'b', 1: 'b'|'c'} $a */
+	public function overlappingUnion(array $a): void
+	{
+		assertType("non-empty-array<'a'|'b'|'c', 0|1>", array_flip($a));
+	}
+
+	/** @param array{0: 'a'|'b', 1: 'c'} $a */
+	public function mixedUnionAndConstant(array $a): void
+	{
+		assertType("array{a?: 0, b?: 0, c: 1}", array_flip($a));
+	}
+}
+
+class ArrayFillKeysUnionValues
+{
+	/** @param array{0: 'a'|'b', 1: 'b'|'c'} $a */
+	public function overlappingUnion(array $a): void
+	{
+		assertType("non-empty-array<'a'|'b'|'c', 'x'>", array_fill_keys($a, 'x'));
+	}
+
+	/** @param array{0: 'a'|'b'|'c', 1: 'a'|'b'|'c', 2: 'a'|'b'|'c'} $a */
+	public function allUnion(array $a): void
+	{
+		assertType("non-empty-array{a?: 'x', b?: 'x', c?: 'x'}", array_fill_keys($a, 'x'));
+	}
+
+	/** @param array{0: 'a'|'b', 1: 'c'} $a */
+	public function mixedUnionAndConstant(array $a): void
+	{
+		assertType("array{a?: 'x', b?: 'x', c: 'x'}", array_fill_keys($a, 'x'));
+	}
+}