diff --git a/mlir/include/mlir/Dialect/MemRef/IR/MemRefOps.td b/mlir/include/mlir/Dialect/MemRef/IR/MemRefOps.td
--- a/mlir/include/mlir/Dialect/MemRef/IR/MemRefOps.td
+++ b/mlir/include/mlir/Dialect/MemRef/IR/MemRefOps.td
@@ -544,7 +544,7 @@
 def MemRef_DimOp : MemRef_Op<"dim", [
     DeclareOpInterfaceMethods<OpAsmOpInterface, ["getAsmResultNames"]>,
     MemRefsNormalizable,
-    Pure,
+    ConditionallySpeculatable, NoMemoryEffect,
     ShapedDimOpInterface]> {
   let summary = "dimension index operation";
   let description = [{
@@ -593,6 +593,9 @@
 
     /// Interface method of ShapedDimOpInterface: Return the dimension.
     OpFoldResult getDimension() { return getIndex(); }
+
+    /// Interface method for ConditionallySpeculatable.
+    Speculation::Speculatability getSpeculatability();
   }];
 
   let hasCanonicalizer = 1;
diff --git a/mlir/include/mlir/Dialect/Tensor/IR/TensorOps.td b/mlir/include/mlir/Dialect/Tensor/IR/TensorOps.td
--- a/mlir/include/mlir/Dialect/Tensor/IR/TensorOps.td
+++ b/mlir/include/mlir/Dialect/Tensor/IR/TensorOps.td
@@ -87,7 +87,7 @@
 
 def Tensor_DimOp : Tensor_Op<"dim", [
     DeclareOpInterfaceMethods<OpAsmOpInterface, ["getAsmResultNames"]>,
-    Pure,
+    ConditionallySpeculatable, NoMemoryEffect,
     ShapedDimOpInterface]> {
   let summary = "dimension index operation";
   let description = [{
@@ -135,6 +135,9 @@
 
     /// Interface method of ShapedDimOpInterface: Return the dimension.
     OpFoldResult getDimension() { return getIndex(); }
+
+    /// Interface method for ConditionallySpeculatable.
+    Speculation::Speculatability getSpeculatability();
   }];
 
   let hasCanonicalizer = 1;
diff --git a/mlir/lib/Dialect/MemRef/IR/MemRefOps.cpp b/mlir/lib/Dialect/MemRef/IR/MemRefOps.cpp
--- a/mlir/lib/Dialect/MemRef/IR/MemRefOps.cpp
+++ b/mlir/lib/Dialect/MemRef/IR/MemRefOps.cpp
@@ -819,6 +819,20 @@
   return {};
 }
 
+Speculation::Speculatability DimOp::getSpeculatability() {
+  auto constantIndex = getConstantIndex();
+  if (!constantIndex)
+    return Speculation::NotSpeculatable;
+
+  auto rankedSourceType = dyn_cast<MemRefType>(getSource().getType());
+  if (!rankedSourceType)
+    return Speculation::NotSpeculatable;
+
+  // The verifier rejects operations that violate this assertion.
+  assert(constantIndex < rankedSourceType.getRank());
+  return Speculation::Speculatable;
+}
+
 LogicalResult DimOp::verify() {
   // Assume unknown index to be in range.
   Optional<int64_t> index = getConstantIndex();
diff --git a/mlir/lib/Dialect/Tensor/IR/TensorOps.cpp b/mlir/lib/Dialect/Tensor/IR/TensorOps.cpp
--- a/mlir/lib/Dialect/Tensor/IR/TensorOps.cpp
+++ b/mlir/lib/Dialect/Tensor/IR/TensorOps.cpp
@@ -328,6 +328,20 @@
   return {};
 }
 
+Speculation::Speculatability DimOp::getSpeculatability() {
+  auto constantIndex = getConstantIndex();
+  if (!constantIndex)
+    return Speculation::NotSpeculatable;
+
+  auto rankedSourceType = dyn_cast<RankedTensorType>(getSource().getType());
+  if (!rankedSourceType)
+    return Speculation::NotSpeculatable;
+
+  // The verifier rejects operations that violate this assertion.
+  assert(constantIndex < rankedSourceType.getRank());
+  return Speculation::Speculatable;
+}
+
 LogicalResult DimOp::verify() {
   // Assume unknown index to be in range.
   Optional<int64_t> index = getConstantIndex();
diff --git a/mlir/test/Transforms/loop-invariant-code-motion.mlir b/mlir/test/Transforms/loop-invariant-code-motion.mlir
--- a/mlir/test/Transforms/loop-invariant-code-motion.mlir
+++ b/mlir/test/Transforms/loop-invariant-code-motion.mlir
@@ -503,3 +503,107 @@
 
   return
 }
+
+// -----
+
+func.func @speculate_tensor_dim_unknown_rank_unknown_dim(
+// CHECK-LABEL: @speculate_tensor_dim_unknown_rank_unknown_dim
+    %t: tensor<*xf32>, %dim_idx: index, %lb: index, %ub: index, %step: index) {
+  // CHECK: scf.for
+  // CHECK-NEXT: tensor.dim
+  scf.for %i = %lb to %ub step %step {
+    %val = tensor.dim %t, %dim_idx : tensor<*xf32>
+  }
+
+  return
+}
+
+func.func @speculate_tensor_dim_known_rank_unknown_dim(
+// CHECK-LABEL: @speculate_tensor_dim_known_rank_unknown_dim
+    %t: tensor<?x?x?x?xf32>, %dim_idx: index, %lb: index, %ub: index, %step: index) {
+  // CHECK: scf.for
+  // CHECK-NEXT: tensor.dim
+  scf.for %i = %lb to %ub step %step {
+    %val = tensor.dim %t, %dim_idx : tensor<?x?x?x?xf32>
+  }
+
+  return
+}
+
+func.func @speculate_tensor_dim_unknown_rank_known_dim(
+// CHECK-LABEL: @speculate_tensor_dim_unknown_rank_known_dim
+    %t: tensor<*xf32>, %dim_idx: index, %lb: index, %ub: index, %step: index) {
+  %c0 = arith.constant 0 : index
+  // CHECK: scf.for
+  // CHECK-NEXT: tensor.dim
+  scf.for %i = %lb to %ub step %step {
+    %val = tensor.dim %t, %c0 : tensor<*xf32>
+  }
+
+  return
+}
+
+func.func @speculate_tensor_dim_known_rank_known_dim_inbounds(
+// CHECK-LABEL: @speculate_tensor_dim_known_rank_known_dim_inbounds
+    %t: tensor<?x?x?x?xf32>, %dim_idx: index, %lb: index, %ub: index, %step: index) {
+  %c1 = arith.constant 1 : index
+  // CHECK: tensor.dim
+  // CHECK-NEXT: scf.for
+  scf.for %i = %lb to %ub step %step {
+    %val = tensor.dim %t, %c1 : tensor<?x?x?x?xf32>
+  }
+
+  return
+}
+
+// -----
+
+func.func @speculate_memref_dim_unknown_rank_unknown_dim(
+// CHECK-LABEL: @speculate_memref_dim_unknown_rank_unknown_dim
+    %t: memref<*xf32>, %dim_idx: index, %lb: index, %ub: index, %step: index) {
+  // CHECK: scf.for
+  // CHECK-NEXT: memref.dim
+  scf.for %i = %lb to %ub step %step {
+    %val = memref.dim %t, %dim_idx : memref<*xf32>
+  }
+
+  return
+}
+
+func.func @speculate_memref_dim_known_rank_unknown_dim(
+// CHECK-LABEL: @speculate_memref_dim_known_rank_unknown_dim
+    %t: memref<?x?x?x?xf32>, %dim_idx: index, %lb: index, %ub: index, %step: index) {
+  // CHECK: scf.for
+  // CHECK-NEXT: memref.dim
+  scf.for %i = %lb to %ub step %step {
+    %val = memref.dim %t, %dim_idx : memref<?x?x?x?xf32>
+  }
+
+  return
+}
+
+func.func @speculate_memref_dim_unknown_rank_known_dim(
+// CHECK-LABEL: @speculate_memref_dim_unknown_rank_known_dim
+    %t: memref<*xf32>, %dim_idx: index, %lb: index, %ub: index, %step: index) {
+  %c0 = arith.constant 0 : index
+  // CHECK: scf.for
+  // CHECK-NEXT: memref.dim
+  scf.for %i = %lb to %ub step %step {
+    %val = memref.dim %t, %c0 : memref<*xf32>
+  }
+
+  return
+}
+
+func.func @speculate_memref_dim_known_rank_known_dim_inbounds(
+// CHECK-LABEL: @speculate_memref_dim_known_rank_known_dim_inbounds
+    %t: memref<?x?x?x?xf32>, %dim_idx: index, %lb: index, %ub: index, %step: index) {
+  %c1 = arith.constant 1 : index
+  // CHECK: memref.dim
+  // CHECK-NEXT: scf.for
+  scf.for %i = %lb to %ub step %step {
+    %val = memref.dim %t, %c1 : memref<?x?x?x?xf32>
+  }
+
+  return
+}