diff --git a/mlir/include/mlir/Analysis/NestedMatcher.h b/mlir/include/mlir/Analysis/NestedMatcher.h
--- a/mlir/include/mlir/Analysis/NestedMatcher.h
+++ b/mlir/include/mlir/Analysis/NestedMatcher.h
@@ -93,8 +93,15 @@
 public:
   NestedPattern(ArrayRef<NestedPattern> nested,
                 FilterFunctionType filter = defaultFilterFunction);
-  NestedPattern(const NestedPattern &) = default;
-  NestedPattern &operator=(const NestedPattern &) = default;
+  NestedPattern(const NestedPattern &other);
+  NestedPattern &operator=(const NestedPattern &other);
+
+  ~NestedPattern() {
+    // Call destructors manually, ArrayRef is non-owning so it wouldn't call
+    // them, but we should free the memory allocated by std::function outside of
+    // the arena allocator.
+    freeNested();
+  }
 
   /// Returns all the top-level matches in `func`.
   void match(FuncOp func, SmallVectorImpl<NestedMatch> *matches) {
@@ -114,6 +121,13 @@
   friend class NestedMatch;
   friend struct State;
 
+  /// Copies the list of nested patterns to the arena allocator associated with
+  /// this pattern.
+  void copyNestedToThis(ArrayRef<NestedPattern> nested);
+
+  /// Calls destructors on nested patterns.
+  void freeNested();
+
   /// Underlying global bump allocator managed by a NestedPatternContext.
   static llvm::BumpPtrAllocator *&allocator();
 
diff --git a/mlir/lib/Analysis/NestedMatcher.cpp b/mlir/lib/Analysis/NestedMatcher.cpp
--- a/mlir/lib/Analysis/NestedMatcher.cpp
+++ b/mlir/lib/Analysis/NestedMatcher.cpp
@@ -39,14 +39,37 @@
   return allocator;
 }
 
+void NestedPattern::copyNestedToThis(ArrayRef<NestedPattern> nested) {
+  if (nested.empty())
+    return;
+
+  auto *newNested = allocator()->Allocate<NestedPattern>(nested.size());
+  std::uninitialized_copy(nested.begin(), nested.end(), newNested);
+  nestedPatterns = ArrayRef<NestedPattern>(newNested, nested.size());
+}
+
+void NestedPattern::freeNested() {
+  for (const auto &p : nestedPatterns)
+    p.~NestedPattern();
+}
+
 NestedPattern::NestedPattern(ArrayRef<NestedPattern> nested,
                              FilterFunctionType filter)
     : nestedPatterns(), filter(filter), skip(nullptr) {
-  if (!nested.empty()) {
-    auto *newNested = allocator()->Allocate<NestedPattern>(nested.size());
-    std::uninitialized_copy(nested.begin(), nested.end(), newNested);
-    nestedPatterns = ArrayRef<NestedPattern>(newNested, nested.size());
-  }
+  copyNestedToThis(nested);
+}
+
+NestedPattern::NestedPattern(const NestedPattern &other)
+    : nestedPatterns(), filter(other.filter), skip(other.skip) {
+  copyNestedToThis(other.nestedPatterns);
+}
+
+NestedPattern &NestedPattern::operator=(const NestedPattern &other) {
+  freeNested();
+  filter = other.filter;
+  skip = other.skip;
+  copyNestedToThis(other.nestedPatterns);
+  return *this;
 }
 
 unsigned NestedPattern::getDepth() const {