Index: include/polly/CodeGen/IslNodeBuilder.h
===================================================================
--- include/polly/CodeGen/IslNodeBuilder.h
+++ include/polly/CodeGen/IslNodeBuilder.h
@@ -412,6 +412,16 @@
   ///                    ids to new access expressions.
   void generateCopyStmt(ScopStmt *Stmt,
                         __isl_keep isl_id_to_ast_expr *NewAccesses);
+
+  /// Materialize a canonical loop induction variable for `L`, which is a loop
+  /// that is *not* present in the Scop.
+  ///
+  /// Note that this is materialized at the point where the `Builder` is
+  /// currently pointing.
+  /// We also populate the `OutsideLoopIterations` map with `L`s SCEV to keep
+  /// track of the induction variable.
+  /// See [Code generation of induction variables of loops outside Scops]
+  Value *materializeNonScopLoopInductionVariable(const Loop *L);
 };
 
 #endif // POLLY_ISL_NODE_BUILDER_H
Index: lib/CodeGen/IslNodeBuilder.cpp
===================================================================
--- lib/CodeGen/IslNodeBuilder.cpp
+++ lib/CodeGen/IslNodeBuilder.cpp
@@ -309,9 +309,17 @@
 
   Values.remove_if([](const Value *V) { return isa<GlobalValue>(V); });
 
+  /// Note: Code generation of induction variables of loops outside Scops
+  ///
   /// Remove loops that contain the scop or that are part of the scop, as they
   /// are considered local. This leaves only loops that are before the scop, but
   /// do not contain the scop itself.
+  /// We ignore loops perfectly contained in the Scop because these are already
+  /// generated at `IslNodeBuilder::addParameters`. These `Loops` are loops
+  /// whose induction variables are referred to by the Scop, but the Scop is not
+  /// fully contained in these Loops. Since there can be many of these,
+  /// we choose to codegen these on-demand.
+  /// @see IslNodeBuilder::materializeNonScopLoopInductionVariable.
   Loops.remove_if([this](const Loop *L) {
     return S.contains(L) || L->contains(S.getEntry());
   });
@@ -627,13 +635,10 @@
   // Create for all loops we depend on values that contain the current loop
   // iteration. These values are necessary to generate code for SCEVs that
   // depend on such loops. As a result we need to pass them to the subfunction.
+  // See [Code generation of induction variables of loops outside Scops]
   for (const Loop *L : Loops) {
-    const SCEV *OuterLIV = SE.getAddRecExpr(SE.getUnknown(Builder.getInt64(0)),
-                                            SE.getUnknown(Builder.getInt64(1)),
-                                            L, SCEV::FlagAnyWrap);
-    Value *V = generateSCEV(OuterLIV);
-    OutsideLoopIterations[L] = SE.getUnknown(V);
-    SubtreeValues.insert(V);
+    Value *LoopInductionVar = materializeNonScopLoopInductionVariable(L);
+    SubtreeValues.insert(LoopInductionVar);
   }
 
   ValueMapT NewValues;
@@ -896,6 +901,17 @@
   Builder.CreateStore(LoadValue, StoreAddr);
 }
 
+Value *IslNodeBuilder::materializeNonScopLoopInductionVariable(const Loop *L) {
+  assert(OutsideLoopIterations.find(L) == OutsideLoopIterations.end() &&
+         "trying to materialize loop induction variable twice");
+  const SCEV *OuterLIV = SE.getAddRecExpr(SE.getUnknown(Builder.getInt64(0)),
+                                          SE.getUnknown(Builder.getInt64(1)), L,
+                                          SCEV::FlagAnyWrap);
+  Value *V = generateSCEV(OuterLIV);
+  OutsideLoopIterations[L] = SE.getUnknown(V);
+  return V;
+}
+
 void IslNodeBuilder::createUser(__isl_take isl_ast_node *User) {
   LoopToScevMapT LTS;
   isl_id *Id;
@@ -1484,11 +1500,7 @@
     L = L->getParentLoop();
 
   while (L != nullptr) {
-    const SCEV *OuterLIV = SE.getAddRecExpr(SE.getUnknown(Builder.getInt64(0)),
-                                            SE.getUnknown(Builder.getInt64(1)),
-                                            L, SCEV::FlagAnyWrap);
-    Value *V = generateSCEV(OuterLIV);
-    OutsideLoopIterations[L] = SE.getUnknown(V);
+    materializeNonScopLoopInductionVariable(L);
     L = L->getParentLoop();
   }