diff --git a/torch/csrc/jit/codegen/cuda/expr_evaluator.cpp b/torch/csrc/jit/codegen/cuda/expr_evaluator.cpp
index 9527520f6041f..6e1c628111113 100644
--- a/torch/csrc/jit/codegen/cuda/expr_evaluator.cpp
+++ b/torch/csrc/jit/codegen/cuda/expr_evaluator.cpp
@@ -61,6 +61,12 @@ void ExpressionEvaluator::bind(Val* value, const IntOrDouble& concrete_value) {
   }
 }
 
+void ExpressionEvaluator::bind(
+    const std::string& name,
+    const IntOrDouble& concrete_value) {
+  known_named_scalars_[name] = concrete_value;
+}
+
 c10::optional<IntOrDouble> ExpressionEvaluator::evaluate(Val* value) {
   if (evaluator_precomputed_values_ != nullptr) {
     return toOptionalIntOrDouble(
diff --git a/torch/csrc/jit/codegen/cuda/expr_evaluator.h b/torch/csrc/jit/codegen/cuda/expr_evaluator.h
index d6001137725d7..4329f9604304b 100644
--- a/torch/csrc/jit/codegen/cuda/expr_evaluator.h
+++ b/torch/csrc/jit/codegen/cuda/expr_evaluator.h
@@ -7,6 +7,7 @@
 
 #include <c10/util/Optional.h>
 
+#include <string>
 #include <unordered_map>
 
 namespace torch {
@@ -30,6 +31,9 @@ class TORCH_CUDA_CU_API ExpressionEvaluator : private OptOutDispatch {
   //! Bind a concrete value to an IR variable
   void bind(Val* value, const IntOrDouble& concrete_value);
 
+  //! Bind a concrete value to a named scalar
+  void bind(const std::string& name, const IntOrDouble& concrete_value);
+
   //! Try to evaluate a Fusion IR value
   c10::optional<IntOrDouble> evaluate(Val* value);
 
diff --git a/torch/csrc/jit/codegen/cuda/lower_bank_conflict.cpp b/torch/csrc/jit/codegen/cuda/lower_bank_conflict.cpp
index 2f29d79f26678..0b97b973f786e 100644
--- a/torch/csrc/jit/codegen/cuda/lower_bank_conflict.cpp
+++ b/torch/csrc/jit/codegen/cuda/lower_bank_conflict.cpp
@@ -1,5 +1,6 @@
 #include <torch/csrc/jit/codegen/cuda/lower_bank_conflict.h>
 
+#include <torch/csrc/jit/codegen/cuda/dynamic_type.h>
 #include <torch/csrc/jit/codegen/cuda/expr_evaluator.h>
 #include <torch/csrc/jit/codegen/cuda/kernel_ir.h>
 #include <torch/csrc/jit/codegen/cuda/kernel_ir_dispatch.h>
@@ -48,23 +49,78 @@ inline int64_t getPhaseSize(int64_t word_size_bytes) {
   return 32;
 }
 
+bool isThreadIdx(const std::string& name) {
+  return name == "threadIdx.x" || name == "threadIdx.y" ||
+      name == "threadIdx.z";
+}
+
+bool isBlockIdx(const std::string& name) {
+  return name == "blockIdx.x" || name == "blockIdx.y" || name == "blockIdx.z";
+}
+
+bool isBlockDim(const std::string& name) {
+  return name == "blockDim.x" && name == "blockDim.y" && name == "blockDim.z";
+}
+
+bool isGridDim(const std::string& name) {
+  return name == "gridDim.x" && name == "gridDim.y" && name == "gridDim.z";
+}
+
+ParallelType getParallelType(const std::string& name) {
+  if (name == "threadIdx.x") {
+    return ParallelType::TIDx;
+  } else if (name == "threadIdx.y") {
+    return ParallelType::TIDy;
+  } else if (name == "threadIdx.z") {
+    return ParallelType::TIDz;
+  } else if (name == "blockIdx.x") {
+    return ParallelType::BIDx;
+  } else if (name == "blockIdx.y") {
+    return ParallelType::BIDy;
+  } else if (name == "blockIdx.z") {
+    return ParallelType::BIDz;
+  }
+  TORCH_INTERNAL_ASSERT(false, "Not a parallel type");
+}
+
 std::vector<int64_t> evaluateAddressesOnFirstPhase(
     kir::TensorIndex* ti,
-    const std::vector<kir::ForLoop*>& for_loops) {
+    const std::vector<kir::ForLoop*>& for_loops,
+    c10::optional<LaunchParams> launch_params,
+    const ExpressionEvaluator& expr_eval_common) {
   std::vector<int64_t> addresses;
   const auto word_size_bytes =
       dataTypeSize(*(ti->getDataType())) * getVectorizeSize(ti);
   int64_t phase_size = getPhaseSize(word_size_bytes);
 
-  for (auto tidx : c10::irange(phase_size)) {
+  if (launch_params.has_value()) {
+    phase_size = std::min<int64_t>(phase_size, launch_params->nThreads());
+  }
+
+  for (int64_t linear_tidx : c10::irange(phase_size)) {
+    int64_t tidx = linear_tidx;
+    int64_t tidy = 0;
+    int64_t tidz = 0;
+    if (launch_params.has_value()) {
+      tidy = tidx / launch_params->bdimx();
+      tidx = tidx % launch_params->bdimx();
+      tidz = tidy / launch_params->bdimy();
+      tidy = tidy % launch_params->bdimy();
+    }
     int64_t index = 0;
-    ExpressionEvaluator expr_eval(ti->fusion());
+    // make a copy of the expression evaluator
+    ExpressionEvaluator expr_eval = expr_eval_common;
+    expr_eval.bind("threadIdx.x", tidx);
+    expr_eval.bind("threadIdx.y", tidy);
+    expr_eval.bind("threadIdx.z", tidz);
     for (auto fl : for_loops) {
-      if (fl->index()->isA<NamedScalar>() &&
-          fl->index()->as<NamedScalar>()->name() == "threadIdx.x") {
-        expr_eval.bind(fl->index(), tidx);
+      if (fl->index()->isA<NamedScalar>()) {
+        auto name = fl->index()->as<NamedScalar>()->name();
+        TORCH_INTERNAL_ASSERT(
+            isThreadIdx(name) || isBlockIdx(name), "unknow loop index");
       } else {
-        expr_eval.bind(fl->index(), 0);
+        auto start = expr_eval.evaluate(fl->start())->as<int64_t>();
+        expr_eval.bind(fl->index(), start);
       }
     }
     for (auto ind : ti->indices()) {
@@ -89,17 +145,97 @@ int getConflictWays(const std::vector<int64_t>& addresses) {
   return conflict;
 }
 
-} // namespace
+class InferLaunchParams : public kir::IrVisitor {
+ public:
+  static c10::optional<LaunchParams> get(
+      const std::vector<Expr*>& exprs,
+      const std::unordered_map<std::string, IntOrDouble>& known_values) {
+    if (exprs.empty()) {
+      return c10::nullopt;
+    }
+    return InferLaunchParams(exprs, known_values).launch_params_;
+  }
+
+ private:
+  InferLaunchParams(
+      const std::vector<Expr*>& exprs,
+      const std::unordered_map<std::string, IntOrDouble>& known_values)
+      : expr_eval_(exprs[0]->fusion()) {
+    for (auto pair : known_values) {
+      expr_eval_.bind(pair.first, pair.second);
+    }
+    handle(exprs);
+  }
+
+  using kir::IrVisitor::handle;
+
+  void handle(Expr* expr) final {
+    if (expr->isA<kir::ForLoop>() || expr->isA<kir::IfThenElse>()) {
+      kir::IrVisitor::handle(expr);
+      return;
+    }
+
+    for (auto fl : for_loops_) {
+      if (fl->index()->isA<NamedScalar>()) {
+        auto name = fl->index()->as<NamedScalar>()->name();
+        if (isThreadIdx(name) || isBlockIdx(name)) {
+          auto ptype = getParallelType(name);
+          auto stop = expr_eval_.evaluate(fl->stop());
+          if (stop.has_value()) {
+            if (!launch_params_.has_value()) {
+              launch_params_ = LaunchParams();
+            }
+            if (launch_params_->getRawVal(ptype) ==
+                LaunchParams::UNINITIALIZED_VAL) {
+              launch_params_->bind(stop->as<int64_t>(), ptype);
+            } else {
+              TORCH_INTERNAL_ASSERT(
+                  launch_params_->getDim(ptype) == stop,
+                  "Unable to infer launch parameters");
+            }
+          }
+        }
+      }
+    }
+  }
+
+  ExpressionEvaluator expr_eval_;
+  c10::optional<LaunchParams> launch_params_;
+};
 
 class BankConflictInfo : public kir::IrVisitor {
  public:
   static std::unordered_map<const Expr*, std::pair<int, int>> get(
-      const std::vector<Expr*>& exprs) {
-    return BankConflictInfo(exprs).bank_conflict_info_;
+      const std::vector<Expr*>& exprs,
+      c10::optional<LaunchParams> launch_params,
+      const std::unordered_map<std::string, IntOrDouble>& known_values) {
+    if (exprs.empty()) {
+      return {};
+    }
+    return BankConflictInfo(exprs, launch_params, known_values)
+        .bank_conflict_info_;
   }
 
  private:
-  BankConflictInfo(const std::vector<Expr*>& exprs) {
+  BankConflictInfo(
+      const std::vector<Expr*>& exprs,
+      c10::optional<LaunchParams> launch_params,
+      const std::unordered_map<std::string, IntOrDouble>& known_values)
+      : launch_params_(launch_params), expr_eval_common_(exprs[0]->fusion()) {
+    expr_eval_common_.bind("blockIdx.x", 0);
+    expr_eval_common_.bind("blockIdx.y", 0);
+    expr_eval_common_.bind("blockIdx.z", 0);
+    if (launch_params.has_value()) {
+      expr_eval_common_.bind("blockDim.x", launch_params->bdimx());
+      expr_eval_common_.bind("blockDim.y", launch_params->bdimy());
+      expr_eval_common_.bind("blockDim.z", launch_params->bdimz());
+      expr_eval_common_.bind("gridDim.x", launch_params->gdimx());
+      expr_eval_common_.bind("gridDim.y", launch_params->gdimy());
+      expr_eval_common_.bind("gridDim.z", launch_params->gdimz());
+    }
+    for (auto pair : known_values) {
+      expr_eval_common_.bind(pair.first, pair.second);
+    }
     handle(exprs);
   }
 
@@ -119,11 +255,17 @@ class BankConflictInfo : public kir::IrVisitor {
       std::pair<int, int> conflict_ways{0, 0};
       if (isSmemTensorIndex(uop->in())) {
         conflict_ways.first = getConflictWays(evaluateAddressesOnFirstPhase(
-            uop->in()->as<kir::TensorIndex>(), for_loops_));
+            uop->in()->as<kir::TensorIndex>(),
+            for_loops_,
+            launch_params_,
+            expr_eval_common_));
       }
       if (isSmemTensorIndex(uop->out())) {
         conflict_ways.second = getConflictWays(evaluateAddressesOnFirstPhase(
-            uop->out()->as<kir::TensorIndex>(), for_loops_));
+            uop->out()->as<kir::TensorIndex>(),
+            for_loops_,
+            launch_params_,
+            expr_eval_common_));
       }
       if (conflict_ways.first > 1 || conflict_ways.second > 1) {
         bank_conflict_info_[expr] = conflict_ways;
@@ -133,11 +275,17 @@ class BankConflictInfo : public kir::IrVisitor {
       std::pair<int, int> conflict_ways{0, 0};
       if (isSmemTensorIndex(ldst->in())) {
         conflict_ways.first = getConflictWays(evaluateAddressesOnFirstPhase(
-            ldst->in()->as<kir::TensorIndex>(), for_loops_));
+            ldst->in()->as<kir::TensorIndex>(),
+            for_loops_,
+            launch_params_,
+            expr_eval_common_));
       }
       if (isSmemTensorIndex(ldst->out())) {
         conflict_ways.second = getConflictWays(evaluateAddressesOnFirstPhase(
-            ldst->out()->as<kir::TensorIndex>(), for_loops_));
+            ldst->out()->as<kir::TensorIndex>(),
+            for_loops_,
+            launch_params_,
+            expr_eval_common_));
       }
       if (conflict_ways.first > 1 || conflict_ways.second > 1) {
         bank_conflict_info_[expr] = conflict_ways;
@@ -146,11 +294,36 @@ class BankConflictInfo : public kir::IrVisitor {
   }
 
   std::unordered_map<const Expr*, std::pair<int, int>> bank_conflict_info_;
+  c10::optional<LaunchParams> launch_params_;
+  ExpressionEvaluator expr_eval_common_;
 };
 
+} // namespace
+
 std::unordered_map<const Expr*, std::pair<int, int>> getBankConflictInfo(
-    kir::Kernel* kernel) {
-  return BankConflictInfo::get(kernel->topLevelExprs());
+    kir::Kernel* kernel,
+    c10::optional<LaunchParams> launch_params,
+    const std::unordered_map<std::string, IntOrDouble>& known_values) {
+  for (auto pair : known_values) {
+    TORCH_CHECK(
+        !isThreadIdx(pair.first),
+        "threadIdx.{x,y,z} should be computed instead of provided");
+    TORCH_CHECK(
+        !isBlockIdx(pair.first),
+        "blockIdx.{x,y,z} should not be provided (they are always zero)");
+    TORCH_CHECK(
+        !isBlockDim(pair.first),
+        "blockDim.{x,y,z} should be provided by launch_params");
+    TORCH_CHECK(
+        !isGridDim(pair.first),
+        "gridDim.{x,y,z} should be provided by launch_params");
+  }
+  if (!launch_params.has_value()) {
+    launch_params =
+        InferLaunchParams::get(kernel->topLevelExprs(), known_values);
+  }
+  return BankConflictInfo::get(
+      kernel->topLevelExprs(), launch_params, known_values);
 }
 
 } // namespace cuda
diff --git a/torch/csrc/jit/codegen/cuda/lower_bank_conflict.h b/torch/csrc/jit/codegen/cuda/lower_bank_conflict.h
index 12c12d4bff4d8..b651c4ed33e22 100644
--- a/torch/csrc/jit/codegen/cuda/lower_bank_conflict.h
+++ b/torch/csrc/jit/codegen/cuda/lower_bank_conflict.h
@@ -1,5 +1,7 @@
 #pragma once
 
+#include <torch/csrc/jit/codegen/cuda/dynamic_type.h>
+#include <torch/csrc/jit/codegen/cuda/executor_launch_params.h>
 #include <torch/csrc/jit/codegen/cuda/ir_base_nodes.h>
 #include <torch/csrc/jit/codegen/cuda/kernel.h>
 
@@ -18,27 +20,25 @@ namespace cuda {
 // nsight compute. This utility currently has the following assumptions and
 // limitations:
 //
-//   1. This utility assumes that `blockDim.x` is large enough to hold one phase
-//   2. This utility assumes that the address only depends on loop variables
-//      (there can not be a thing like `T0.stride[0]`, `blockDim.x`)
-//   3. This utility assumes that the data of the tensor is accessed by
+//   1. This utility assumes that the data of the tensor is accessed by
 //      `T0[index]`, where `index` is the one stored in the `TensorIndex`
 //      object.
-//   4. This utility only checks the first iteration, and the start of all
-//      loop variables are assumed to be `0` (if we have something like
+//   2. This utility only checks the first iteration. If we have something like
 //      `T1_s[tidx, 5]`, then different iterations should have different
-//      results, which this utility will not be able to handle all of them now)
-//   5. This utility assumes that all tensors are independent, which means:
-//      5.1 All shared memory tensors are allocated starting from a multiple of
+//      conflictions, which will not be evaluated for all of them
+//   3. This utility assumes that all tensors are independent, which means:
+//      3.1 All shared memory tensors are allocated starting from a multiple of
 //          4*32 bytes
-//      5.2 The only source of bank confliction is from within a tensor.
+//      3.2 The only source of bank confliction is from within a tensor.
 //          There is no bank conflict between different tensors.
 //
 // Also note that this utility will not provide accurate estimation if the above
 // assumptions are satisfied
 
 std::unordered_map<const Expr*, std::pair<int, int>> getBankConflictInfo(
-    kir::Kernel* kernel);
+    kir::Kernel* kernel,
+    c10::optional<LaunchParams> launch_params = c10::nullopt,
+    const std::unordered_map<std::string, IntOrDouble>& known_values = {});
 
 } // namespace cuda
 } // namespace fuser
diff --git a/torch/csrc/jit/codegen/cuda/test/test_gpu_transpose.cpp b/torch/csrc/jit/codegen/cuda/test/test_gpu_transpose.cpp
index 8c00fea08489c..b10360f00315e 100644
--- a/torch/csrc/jit/codegen/cuda/test/test_gpu_transpose.cpp
+++ b/torch/csrc/jit/codegen/cuda/test/test_gpu_transpose.cpp
@@ -1041,6 +1041,7 @@ TEST_F(NVFuserTest, FusionTransposeBankConflict1_CUDA) {
 
   auto bank_conflict_info = fusion.bankConflictInfo();
 
+  TORCH_CHECK(!bank_conflict_info.empty());
   for (auto info : bank_conflict_info) {
     std::pair<int, int> expect{32, 0};
     TORCH_CHECK(info.second == expect);
@@ -1065,6 +1066,7 @@ TEST_F(NVFuserTest, FusionTransposeBankConflict2_CUDA) {
 
   auto bank_conflict_info = fusion.bankConflictInfo();
 
+  TORCH_CHECK(!bank_conflict_info.empty());
   for (auto info : bank_conflict_info) {
     std::pair<int, int> expect{0, 32};
     TORCH_CHECK(info.second == expect);
@@ -1089,6 +1091,7 @@ TEST_F(NVFuserTest, FusionTransposeBankConflict3_CUDA) {
 
   auto bank_conflict_info = fusion.bankConflictInfo();
 
+  TORCH_CHECK(!bank_conflict_info.empty());
   for (auto info : bank_conflict_info) {
     std::pair<int, int> expect{8, 0};
     TORCH_CHECK(info.second == expect);
@@ -1129,6 +1132,7 @@ TEST_F(NVFuserTest, FusionTransposeBankConflict4_CUDA) {
 
   auto bank_conflict_info = fusion.bankConflictInfo();
 
+  TORCH_CHECK(!bank_conflict_info.empty());
   for (auto info : bank_conflict_info) {
     std::pair<int, int> expect1{0, 8};
     std::pair<int, int> expect2{8, 4};
@@ -1139,6 +1143,118 @@ TEST_F(NVFuserTest, FusionTransposeBankConflict4_CUDA) {
   }
 }
 
+TEST_F(NVFuserTest, FusionTransposeBankConflict5_CUDA) {
+  Fusion fusion;
+  FusionGuard fg(&fusion);
+
+  auto tv0 = makeConcreteTensor({1024, 32, 32});
+  fusion.addInput(tv0);
+  auto tv1 = set(tv0);
+  auto tv2 = transpose(tv1, 1, 2);
+  auto tv3 = set(tv2);
+  fusion.addOutput(tv3);
+
+  tv1->setMemoryType(MemoryType::Shared);
+  tv1->axis(2)->parallelize(ParallelType::TIDx);
+  tv2->axis(2)->parallelize(ParallelType::TIDx);
+  tv3->axis(2)->parallelize(ParallelType::TIDx);
+  tv1->axis(0)->parallelize(ParallelType::BIDx);
+  tv2->axis(0)->parallelize(ParallelType::BIDx);
+  tv3->axis(0)->parallelize(ParallelType::BIDx);
+
+  auto bank_conflict_info = fusion.bankConflictInfo();
+
+  TORCH_CHECK(!bank_conflict_info.empty());
+  for (auto info : bank_conflict_info) {
+    std::pair<int, int> expect{32, 0};
+    TORCH_CHECK(info.second == expect);
+  }
+}
+
+TEST_F(NVFuserTest, FusionTransposeBankConflict6_CUDA) {
+  Fusion fusion;
+  FusionGuard fg(&fusion);
+
+  auto tv0 = makeConcreteTensor({1024, 32, 32});
+  fusion.addInput(tv0);
+  auto tv1 = set(tv0);
+  auto tv2 = transpose(tv1, 1, 2);
+  auto tv3 = set(tv2);
+  fusion.addOutput(tv3);
+
+  tv1->setMemoryType(MemoryType::Shared);
+  tv1->axis(2)->parallelize(ParallelType::TIDy);
+  tv2->axis(2)->parallelize(ParallelType::TIDy);
+  tv3->axis(2)->parallelize(ParallelType::TIDy);
+  tv1->axis(0)->parallelize(ParallelType::BIDx);
+  tv2->axis(0)->parallelize(ParallelType::BIDx);
+  tv3->axis(0)->parallelize(ParallelType::BIDx);
+
+  auto bank_conflict_info = fusion.bankConflictInfo();
+
+  TORCH_CHECK(!bank_conflict_info.empty());
+  for (auto info : bank_conflict_info) {
+    std::pair<int, int> expect{32, 0};
+    TORCH_CHECK(info.second == expect);
+  }
+}
+
+TEST_F(NVFuserTest, FusionTransposeBankConflict7_CUDA) {
+  Fusion fusion;
+  FusionGuard fg(&fusion);
+
+  auto tv0 = makeConcreteTensor({1024, 8, 8});
+  fusion.addInput(tv0);
+  auto tv1 = set(tv0);
+  auto tv2 = transpose(tv1, 1, 2);
+  auto tv3 = set(tv2);
+  fusion.addOutput(tv3);
+
+  tv1->setMemoryType(MemoryType::Shared);
+  tv1->axis(1)->parallelize(ParallelType::TIDx);
+  tv2->axis(1)->parallelize(ParallelType::TIDx);
+  tv3->axis(1)->parallelize(ParallelType::TIDx);
+  tv1->axis(2)->parallelize(ParallelType::TIDy);
+  tv2->axis(2)->parallelize(ParallelType::TIDy);
+  tv3->axis(2)->parallelize(ParallelType::TIDy);
+  tv1->axis(0)->parallelize(ParallelType::BIDx);
+  tv2->axis(0)->parallelize(ParallelType::BIDx);
+  tv3->axis(0)->parallelize(ParallelType::BIDx);
+
+  auto bank_conflict_info = fusion.bankConflictInfo();
+
+  TORCH_CHECK(!bank_conflict_info.empty());
+  for (auto info : bank_conflict_info) {
+    std::pair<int, int> expect{0, 2};
+    TORCH_CHECK(info.second == expect);
+  }
+}
+
+TEST_F(NVFuserTest, FusionTransposeBankConflict8_CUDA) {
+  Fusion fusion;
+  FusionGuard fg(&fusion);
+
+  auto tv0 = makeConcreteTensor({1024, 8, 8});
+  fusion.addInput(tv0);
+  auto tv1 = set(tv0);
+  auto tv2 = transpose(tv1, 1, 2);
+  auto tv3 = set(tv2);
+  fusion.addOutput(tv3);
+
+  tv1->setMemoryType(MemoryType::Shared);
+  tv1->axis(2)->parallelize(ParallelType::TIDx);
+  tv2->axis(2)->parallelize(ParallelType::TIDy);
+  tv3->axis(2)->parallelize(ParallelType::TIDy);
+  tv1->axis(0)->parallelize(ParallelType::BIDx);
+  tv2->axis(0)->parallelize(ParallelType::BIDx);
+  tv3->axis(0)->parallelize(ParallelType::BIDx);
+
+  auto bank_conflict_info = fusion.bankConflictInfo();
+
+  // no bank confliction
+  TORCH_CHECK(bank_conflict_info.empty());
+}
+
 } // namespace jit
 } // namespace torch
 #endif // #if defined(USE_CUDA)