diff --git a/mlir/include/mlir/Analysis/DataFlowFramework.h b/mlir/include/mlir/Analysis/DataFlowFramework.h
index 49862927caff2..654d888174089 100644
--- a/mlir/include/mlir/Analysis/DataFlowFramework.h
+++ b/mlir/include/mlir/Analysis/DataFlowFramework.h
@@ -658,6 +658,11 @@ class DataFlowAnalysis {
     return solver.getOrCreateState<StateT>(anchor);
   }
 
+  /// Add irrelevant program point.
+  void addIrrelevantPoint(ProgramPoint *point) {
+    irrelevantPoints.insert(point);
+  }
+
   /// Get a read-only analysis state for the given point and create a dependency
   /// on `dependent`. If the return state is updated elsewhere, this analysis is
   /// re-invoked on the dependent.
@@ -695,6 +700,9 @@ class DataFlowAnalysis {
   StringRef debugName;
 #endif // LLVM_ENABLE_ABI_BREAKING_CHECKS
 
+  /// Program points shouldn't analyzed by this analysis.
+  DenseSet<ProgramPoint *> irrelevantPoints;
+
 private:
   /// The parent data-flow solver.
   DataFlowSolver &solver;
diff --git a/mlir/lib/Analysis/DataFlow/DenseAnalysis.cpp b/mlir/lib/Analysis/DataFlow/DenseAnalysis.cpp
index d05374f667a51..3bbd95982be75 100644
--- a/mlir/lib/Analysis/DataFlow/DenseAnalysis.cpp
+++ b/mlir/lib/Analysis/DataFlow/DenseAnalysis.cpp
@@ -104,7 +104,11 @@ void AbstractDenseForwardDataFlowAnalysis::visitCallOperation(
 
 LogicalResult
 AbstractDenseForwardDataFlowAnalysis::processOperation(Operation *op) {
+  // Skip irrelavant program points.
   ProgramPoint *point = getProgramPointAfter(op);
+  if (irrelevantPoints.contains(point))
+    return success();
+
   // If the containing block is not executable, bail out.
   if (op->getBlock() != nullptr &&
       !getOrCreateFor<Executable>(point, getProgramPointBefore(op->getBlock()))
@@ -333,7 +337,11 @@ void AbstractDenseBackwardDataFlowAnalysis::visitCallOperation(
 
 LogicalResult
 AbstractDenseBackwardDataFlowAnalysis::processOperation(Operation *op) {
+  // Skip irrelavant program points.
   ProgramPoint *point = getProgramPointBefore(op);
+  if (irrelevantPoints.contains(point))
+    return success();
+
   // If the containing block is not executable, bail out.
   if (op->getBlock() != nullptr &&
       !getOrCreateFor<Executable>(point, getProgramPointBefore(op->getBlock()))
diff --git a/mlir/test/lib/Analysis/DataFlow/TestDenseBackwardDataFlowAnalysis.cpp b/mlir/test/lib/Analysis/DataFlow/TestDenseBackwardDataFlowAnalysis.cpp
index d57b41c41de64..881deff0ef4a5 100644
--- a/mlir/test/lib/Analysis/DataFlow/TestDenseBackwardDataFlowAnalysis.cpp
+++ b/mlir/test/lib/Analysis/DataFlow/TestDenseBackwardDataFlowAnalysis.cpp
@@ -147,6 +147,7 @@ LogicalResult NextAccessAnalysis::visitOperation(Operation *op,
 
 void NextAccessAnalysis::buildOperationEquivalentLatticeAnchor(Operation *op) {
   if (isMemoryEffectFree(op)) {
+    addIrrelevantPoint(getProgramPointBefore(op));
     unionLatticeAnchors<NextAccess>(getProgramPointBefore(op),
                                     getProgramPointAfter(op));
   }
diff --git a/mlir/test/lib/Analysis/DataFlow/TestDenseForwardDataFlowAnalysis.cpp b/mlir/test/lib/Analysis/DataFlow/TestDenseForwardDataFlowAnalysis.cpp
index a88ed7f8dea8b..462bea0c6bcc9 100644
--- a/mlir/test/lib/Analysis/DataFlow/TestDenseForwardDataFlowAnalysis.cpp
+++ b/mlir/test/lib/Analysis/DataFlow/TestDenseForwardDataFlowAnalysis.cpp
@@ -154,6 +154,7 @@ LogicalResult LastModifiedAnalysis::visitOperation(
 void LastModifiedAnalysis::buildOperationEquivalentLatticeAnchor(
     Operation *op) {
   if (isMemoryEffectFree(op)) {
+    addIrrelevantPoint(getProgramPointAfter(op));
     unionLatticeAnchors<LastModification>(getProgramPointBefore(op),
                                           getProgramPointAfter(op));
   }