diff --git a/mlir/include/mlir/Analysis/DataFlow/DenseAnalysis.h b/mlir/include/mlir/Analysis/DataFlow/DenseAnalysis.h
--- a/mlir/include/mlir/Analysis/DataFlow/DenseAnalysis.h
+++ b/mlir/include/mlir/Analysis/DataFlow/DenseAnalysis.h
@@ -42,10 +42,6 @@
   /// Reset the dense lattice to a pessimistic value. This occurs when the
   /// analysis cannot reason about the data-flow.
   virtual ChangeResult reset() = 0;
-
-  /// Returns true if the lattice state has reached a pessimistic fixpoint. That
-  /// is, no further modifications to the lattice can occur.
-  virtual bool isAtFixpoint() const = 0;
 };
 
 //===----------------------------------------------------------------------===//
diff --git a/mlir/include/mlir/Analysis/DataFlow/SparseAnalysis.h b/mlir/include/mlir/Analysis/DataFlow/SparseAnalysis.h
--- a/mlir/include/mlir/Analysis/DataFlow/SparseAnalysis.h
+++ b/mlir/include/mlir/Analysis/DataFlow/SparseAnalysis.h
@@ -38,10 +38,6 @@
   /// if the value of the lattice changed.
   virtual ChangeResult join(const AbstractSparseLattice &rhs) = 0;
 
-  /// Returns true if the lattice element is at fixpoint and further calls to
-  /// `join` will not update the value of the element.
-  virtual bool isAtFixpoint() const = 0;
-
   /// Mark the lattice element as having reached a pessimistic fixpoint. This
   /// means that the lattice may potentially have conflicting value states, and
   /// only the most conservative value should be relied on.
@@ -103,19 +99,14 @@
     return markPessimisticFixpoint();
   }
 
-  /// Returns true if the lattice has reached a fixpoint. A fixpoint is when
-  /// the information optimistically assumed to be true is the same as the
-  /// information known to be true.
-  bool isAtFixpoint() const override { return optimisticValue == knownValue; }
-
   /// Join the information contained in the 'rhs' lattice into this
   /// lattice. Returns if the state of the current lattice changed.
   ChangeResult join(const AbstractSparseLattice &rhs) override {
     const Lattice<ValueT> &rhsLattice =
         static_cast<const Lattice<ValueT> &>(rhs);
 
-    // If we are at a fixpoint, or rhs is uninitialized, there is nothing to do.
-    if (isAtFixpoint() || rhsLattice.isUninitialized())
+    // If rhs is uninitialized, there is nothing to do.
+    if (rhsLattice.isUninitialized())
       return ChangeResult::NoChange;
 
     // Join the rhs value into this lattice.
@@ -150,7 +141,7 @@
   /// means that the lattice may potentially have conflicting value states,
   /// and only the conservatively known value state should be relied on.
   ChangeResult markPessimisticFixpoint() override {
-    if (isAtFixpoint())
+    if (optimisticValue == knownValue)
       return ChangeResult::NoChange;
 
     // For this fixed point, we take whatever we knew to be true and set that
diff --git a/mlir/lib/Analysis/DataFlow/DenseAnalysis.cpp b/mlir/lib/Analysis/DataFlow/DenseAnalysis.cpp
--- a/mlir/lib/Analysis/DataFlow/DenseAnalysis.cpp
+++ b/mlir/lib/Analysis/DataFlow/DenseAnalysis.cpp
@@ -49,8 +49,6 @@
 
   // Get the dense lattice to update.
   AbstractDenseLattice *after = getLattice(op);
-  if (after->isAtFixpoint())
-    return;
 
   // If this op implements region control-flow, then control-flow dictates its
   // transfer function.
@@ -91,8 +89,6 @@
 
   // Get the dense lattice to update.
   AbstractDenseLattice *after = getLattice(block);
-  if (after->isAtFixpoint())
-    return;
 
   // The dense lattices of entry blocks are set by region control-flow or the
   // callgraph.
diff --git a/mlir/lib/Analysis/DataFlow/SparseAnalysis.cpp b/mlir/lib/Analysis/DataFlow/SparseAnalysis.cpp
--- a/mlir/lib/Analysis/DataFlow/SparseAnalysis.cpp
+++ b/mlir/lib/Analysis/DataFlow/SparseAnalysis.cpp
@@ -87,16 +87,10 @@
   // Get the result lattices.
   SmallVector<AbstractSparseLattice *> resultLattices;
   resultLattices.reserve(op->getNumResults());
-  // Track whether all results have reached their fixpoint.
-  bool allAtFixpoint = true;
   for (Value result : op->getResults()) {
     AbstractSparseLattice *resultLattice = getLatticeElement(result);
-    allAtFixpoint &= resultLattice->isAtFixpoint();
     resultLattices.push_back(resultLattice);
   }
-  // If all result lattices have reached a fixpoint, there is nothing to do.
-  if (allAtFixpoint)
-    return;
 
   // The results of a region branch operation are determined by control-flow.
   if (auto branch = dyn_cast<RegionBranchOpInterface>(op)) {
@@ -145,16 +139,10 @@
   // Get the argument lattices.
   SmallVector<AbstractSparseLattice *> argLattices;
   argLattices.reserve(block->getNumArguments());
-  bool allAtFixpoint = true;
   for (BlockArgument argument : block->getArguments()) {
     AbstractSparseLattice *argLattice = getLatticeElement(argument);
-    allAtFixpoint &= argLattice->isAtFixpoint();
     argLattices.push_back(argLattice);
   }
-  // If all argument lattices have reached their fixpoints, then there is
-  // nothing to do.
-  if (allAtFixpoint)
-    return;
 
   // The argument lattices of entry blocks are set by region control-flow or the
   // callgraph.
diff --git a/mlir/test/lib/Analysis/DataFlow/TestDenseDataFlowAnalysis.cpp b/mlir/test/lib/Analysis/DataFlow/TestDenseDataFlowAnalysis.cpp
--- a/mlir/test/lib/Analysis/DataFlow/TestDenseDataFlowAnalysis.cpp
+++ b/mlir/test/lib/Analysis/DataFlow/TestDenseDataFlowAnalysis.cpp
@@ -73,9 +73,6 @@
     return ChangeResult::Change;
   }
 
-  /// The lattice is never at a fixpoint.
-  bool isAtFixpoint() const override { return false; }
-
   /// Join the last modifications.
   ChangeResult join(const AbstractDenseLattice &lattice) override {
     const auto &rhs = static_cast<const LastModification &>(lattice);