diff --git a/llvm/lib/Transforms/Scalar/LoopInterchange.cpp b/llvm/lib/Transforms/Scalar/LoopInterchange.cpp
index 70e9eee5339a7..08446ccaa9fca 100644
--- a/llvm/lib/Transforms/Scalar/LoopInterchange.cpp
+++ b/llvm/lib/Transforms/Scalar/LoopInterchange.cpp
@@ -17,8 +17,8 @@
 #include "llvm/ADT/SmallSet.h"
 #include "llvm/ADT/SmallVector.h"
 #include "llvm/ADT/Statistic.h"
+#include "llvm/ADT/StringMap.h"
 #include "llvm/ADT/StringRef.h"
-#include "llvm/ADT/StringSet.h"
 #include "llvm/Analysis/DependenceAnalysis.h"
 #include "llvm/Analysis/LoopCacheAnalysis.h"
 #include "llvm/Analysis/LoopInfo.h"
@@ -70,6 +70,13 @@ namespace {
 
 using LoopVector = SmallVector<Loop *, 8>;
 
+/// A list of direction vectors. Each entry represents a direction vector
+/// corresponding to one or more dependencies existing in the loop nest. The
+/// length of all direction vectors is equal and is N + 1, where N is the depth
+/// of the loop nest. The first N elements correspond to the dependency
+/// direction of each N loops. The last one indicates whether this entry is
+/// forward dependency ('<') or not ('*'). The term "forward" aligns with what
+/// is defined in LoopAccessAnalysis.
 // TODO: Check if we can use a sparse matrix here.
 using CharMatrix = std::vector<std::vector<char>>;
 
@@ -126,11 +133,33 @@ static bool noDuplicateRulesAndIgnore(ArrayRef<RuleTy> Rules) {
 
 static void printDepMatrix(CharMatrix &DepMatrix) {
   for (auto &Row : DepMatrix) {
-    for (auto D : Row)
+    // Drop the last element because it is a flag indicating whether this is
+    // forward dependency or not, which doesn't affect the legality check.
+    for (char D : drop_end(Row))
       LLVM_DEBUG(dbgs() << D << " ");
     LLVM_DEBUG(dbgs() << "\n");
   }
 }
+
+/// Return true if \p Src appears before \p Dst in the same basic block.
+/// Precondition: \p Src and \Dst are distinct instructions within the same
+/// basic block.
+static bool inThisOrder(const Instruction *Src, const Instruction *Dst) {
+  assert(Src->getParent() == Dst->getParent() && Src != Dst &&
+         "Expected Src and Dst to be different instructions in the same BB");
+
+  bool FoundSrc = false;
+  for (const Instruction &I : *(Src->getParent())) {
+    if (&I == Src) {
+      FoundSrc = true;
+      continue;
+    }
+    if (&I == Dst)
+      return FoundSrc;
+  }
+
+  llvm_unreachable("Dst not found");
+}
 #endif
 
 static bool populateDependencyMatrix(CharMatrix &DepMatrix, unsigned Level,
@@ -174,7 +203,10 @@ static bool populateDependencyMatrix(CharMatrix &DepMatrix, unsigned Level,
     return false;
   }
   ValueVector::iterator I, IE, J, JE;
-  StringSet<> Seen;
+
+  // Manage direction vectors that are already seen. Map each direction vector
+  // to an index of DepMatrix at which it is stored.
+  StringMap<unsigned> Seen;
 
   for (I = MemInstr.begin(), IE = MemInstr.end(); I != IE; ++I) {
     for (J = I, JE = MemInstr.end(); J != JE; ++J) {
@@ -228,9 +260,49 @@ static bool populateDependencyMatrix(CharMatrix &DepMatrix, unsigned Level,
           Dep.push_back('I');
         }
 
+        // Test whether the dependency is forward or not.
+        bool IsKnownForward = true;
+        if (Src->getParent() != Dst->getParent()) {
+          // In general, when Src and Dst are in different BBs, the execution
+          // order of them within a single iteration is not guaranteed. Treat
+          // conservatively as not-forward dependency in this case.
+          IsKnownForward = false;
+        } else {
+          // Src and Dst are in the same BB. If they are the different
+          // instructions, Src should appear before Dst in the BB as they are
+          // stored to MemInstr in that order.
+          assert((Src == Dst || inThisOrder(Src, Dst)) &&
+                 "Unexpected instructions");
+
+          // If the Dependence object is reversed (due to normalization), it
+          // represents the dependency from Dst to Src, meaning it is a backward
+          // dependency. Otherwise it should be a forward dependency.
+          bool IsReversed = D->getSrc() != Src;
+          if (IsReversed)
+            IsKnownForward = false;
+        }
+
+        // Initialize the last element. Assume forward dependencies only; it
+        // will be updated later if there is any non-forward dependency.
+        Dep.push_back('<');
+
+        // The last element should express the "summary" among one or more
+        // direction vectors whose first N elements are the same (where N is
+        // the depth of the loop nest). Hence we exclude the last element from
+        // the Seen map.
+        auto [Ite, Inserted] = Seen.try_emplace(
+            StringRef(Dep.data(), Dep.size() - 1), DepMatrix.size());
+
         // Make sure we only add unique entries to the dependency matrix.
-        if (Seen.insert(StringRef(Dep.data(), Dep.size())).second)
+        if (Inserted)
           DepMatrix.push_back(Dep);
+
+        // If we cannot prove that this dependency is forward, change the last
+        // element of the corresponding entry. Since a `[... *]` dependency
+        // includes a `[... <]` dependency, we do not need to keep both and
+        // change the existing entry instead.
+        if (!IsKnownForward)
+          DepMatrix[Ite->second].back() = '*';
       }
     }
   }
@@ -281,11 +353,12 @@ static bool isLegalToInterChangeLoops(CharMatrix &DepMatrix,
       continue;
 
     // Check if the direction vector is lexicographically positive (or zero)
-    // for both before/after exchanged.
-    if (isLexicographicallyPositive(Cur, OuterLoopId, Cur.size()) == false)
+    // for both before/after exchanged. Ignore the last element because it
+    // doesn't affect the legality.
+    if (isLexicographicallyPositive(Cur, OuterLoopId, Cur.size() - 1) == false)
       return false;
     std::swap(Cur[InnerLoopId], Cur[OuterLoopId]);
-    if (isLexicographicallyPositive(Cur, OuterLoopId, Cur.size()) == false)
+    if (isLexicographicallyPositive(Cur, OuterLoopId, Cur.size() - 1) == false)
       return false;
   }
   return true;
@@ -1334,22 +1407,35 @@ LoopInterchangeProfitability::isProfitablePerInstrOrderCost() {
 static bool canVectorize(const CharMatrix &DepMatrix, unsigned LoopId) {
   for (const auto &Dep : DepMatrix) {
     char Dir = Dep[LoopId];
-    if (Dir != 'I' && Dir != '=')
-      return false;
+    char DepType = Dep.back();
+    assert((DepType == '<' || DepType == '*') &&
+           "Unexpected element in dependency vector");
+
+    // There are no loop-carried dependencies.
+    if (Dir == '=' || Dir == 'I')
+      continue;
+
+    // DepType being '<' means that this direction vector represents a forward
+    // dependency. In principle, a loop with '<' direction can be vectorized in
+    // this case.
+    if (Dir == '<' && DepType == '<')
+      continue;
+
+    // We cannot prove that the loop is vectorizable.
+    return false;
   }
   return true;
 }
 
 std::optional<bool> LoopInterchangeProfitability::isProfitableForVectorization(
     unsigned InnerLoopId, unsigned OuterLoopId, CharMatrix &DepMatrix) {
-  // If the outer loop is not loop independent it is not profitable to move
-  // this to inner position, since doing so would not enable inner loop
-  // parallelism.
+  // If the outer loop cannot be vectorized, it is not profitable to move this
+  // to inner position.
   if (!canVectorize(DepMatrix, OuterLoopId))
     return false;
 
-  // If inner loop has dependence and outer loop is loop independent then it is
-  // profitable to interchange to enable inner loop parallelism.
+  // If the inner loop cannot be vectorized but the outer loop can be, then it
+  // is profitable to interchange to enable inner loop parallelism.
   if (!canVectorize(DepMatrix, InnerLoopId))
     return true;
 
diff --git a/llvm/test/Transforms/LoopInterchange/profitability-vectorization-heuristic.ll b/llvm/test/Transforms/LoopInterchange/profitability-vectorization-heuristic.ll
index 9c113d4570e4d..4194849784054 100644
--- a/llvm/test/Transforms/LoopInterchange/profitability-vectorization-heuristic.ll
+++ b/llvm/test/Transforms/LoopInterchange/profitability-vectorization-heuristic.ll
@@ -5,6 +5,8 @@
 @A = dso_local global [256 x [256 x float]] zeroinitializer
 @B = dso_local global [256 x [256 x float]] zeroinitializer
 @C = dso_local global [256 x [256 x float]] zeroinitializer
+@D = global [256 x [256 x [256 x float]]] zeroinitializer
+@E = global [256 x [256 x [256 x float]]] zeroinitializer
 
 ; Check that the below loops are exchanged for vectorization.
 ;
@@ -64,15 +66,13 @@ exit:
 ;   for (int j = 1; j < 256; j++)
 ;     A[i][j-1] = A[i][j] + B[i][j];
 ;
-; FIXME: These loops are exchanged at this time due to the problem in
-; profitability heuristic calculation for vectorization.
 
-; CHECK:      --- !Passed
+; CHECK:      --- !Missed
 ; CHECK-NEXT: Pass:            loop-interchange
-; CHECK-NEXT: Name:            Interchanged
+; CHECK-NEXT: Name:            InterchangeNotProfitable
 ; CHECK-NEXT: Function:        interchange_unnecesasry_for_vectorization
 ; CHECK-NEXT: Args:
-; CHECK-NEXT:   - String:          Loop interchanged with enclosing loop.
+; CHECK-NEXT:   - String:          Insufficient information to calculate the cost of loop for interchange.
 define void @interchange_unnecesasry_for_vectorization() {
 entry:
   br label %for.i.header
@@ -103,3 +103,134 @@ for.i.inc:
 exit:
   ret void
 }
+
+; Check that the below loops are exchanged to allow innermost loop
+; vectorization. We cannot vectorize the j-loop because it has a lexically
+; backward dependency, but the i-loop can be vectorized because all the
+; loop-carried dependencies are lexically forward. LoopVectorize currently only
+; vectorizes innermost loop, hence move the i-loop to that position.
+;
+; for (int i = 0; i < 255; i++) {
+;   for (int j = 1; j < 256; j++) {
+;     A[i][j] = A[i][j-1] + B[i][j];
+;     C[i][j] += C[i+1][j];
+;   }
+; }
+;
+
+; CHECK:      --- !Passed
+; CHECK-NEXT: Pass:            loop-interchange
+; CHECK-NEXT: Name:            Interchanged
+; CHECK-NEXT: Function:        interchange_necessary_for_vectorization2
+; CHECK-NEXT: Args:
+; CHECK-NEXT:   - String:          Loop interchanged with enclosing loop.
+define void @interchange_necessary_for_vectorization2() {
+entry:
+  br label %for.i.header
+
+for.i.header:
+  %i = phi i64 [ 1, %entry ], [ %i.next, %for.i.inc ]
+  %i.inc = add i64 %i, 1
+  br label %for.j.body
+
+for.j.body:
+  %j = phi i64 [ 1, %for.i.header ], [ %j.next, %for.j.body ]
+  %j.dec = add i64 %j, -1
+  %a.load.index = getelementptr [256 x [256 x float]], ptr @A, i64 0, i64 %i, i64 %j.dec
+  %b.index = getelementptr [256 x [256 x float]], ptr @B, i64 0, i64 %i, i64 %j
+  %c.load.index = getelementptr [256 x [256 x float]], ptr @C, i64 0, i64 %i.inc, i64 %j
+  %c.store.index = getelementptr [256 x [256 x float]], ptr @C, i64 0, i64 %i, i64 %j
+  %a = load float, ptr %a.load.index
+  %b = load float, ptr %b.index
+  %c0 = load float, ptr %c.load.index
+  %c1 = load float, ptr %c.store.index
+  %add.0 = fadd float %a, %b
+  %a.store.index = getelementptr [256 x [256 x float]], ptr @A, i64 0, i64 %i, i64 %j
+  store float %add.0, ptr %a.store.index
+  %add.1 = fadd float %c0, %c1
+  store float %add.1, ptr %c.store.index
+  %j.next = add i64 %j, 1
+  %cmp.j = icmp eq i64 %j.next, 256
+  br i1 %cmp.j, label %for.i.inc, label %for.j.body
+
+for.i.inc:
+  %i.next = add i64 %i, 1
+  %cmp.i = icmp eq i64 %i.next, 255
+  br i1 %cmp.i, label %exit, label %for.i.header
+
+exit:
+  ret void
+}
+
+; Check that no interchange is performed for the following loop. Interchanging
+; the j-loop and k-loop makes the innermost loop vectorizble, since the j-loop
+; has only forward dependencies. However, at the moment, a loop body consisting
+; of multiple BBs is handled pesimistically. Hence the j-loop isn't moved to
+; the innermost place.
+;
+; for (int i = 0; i < 255; i++) {
+;   for (int j = 0; j < 255; j++) {
+;     for (int k = 0; k < 128; k++) {
+;       E[i][j][k] = D[i+1][j+1][2*k];
+;       if (cond)
+;         D[i][j][k+1] = 1.0;
+;   }
+; }
+
+; CHECK:      --- !Missed
+; CHECK-NEXT: Pass:            loop-interchange
+; CHECK-NEXT: Name:            InterchangeNotProfitable
+; CHECK-NEXT: Function:        multiple_BBs_in_loop
+; CHECK-NEXT: Args:
+; CHECK-NEXT:   - String:          Interchanging loops is not considered to improve cache locality nor vectorization.
+; CHECK:      --- !Missed
+; CHECK-NEXT: Pass:            loop-interchange
+; CHECK-NEXT: Name:            InterchangeNotProfitable
+; CHECK-NEXT: Function:        multiple_BBs_in_loop
+; CHECK-NEXT: Args:
+; CHECK-NEXT:   - String:          Interchanging loops is not considered to improve cache locality nor vectorization.
+define void @multiple_BBs_in_loop() {
+entry:
+  br label %for.i.header
+
+for.i.header:
+  %i = phi i64 [ 0, %entry ], [ %i.inc, %for.i.inc ]
+  %i.inc = add i64 %i, 1
+  br label %for.j.header
+
+for.j.header:
+  %j = phi i64 [ 0, %for.i.header ], [ %j.inc, %for.j.inc ]
+  %j.inc = add i64 %j, 1
+  br label %for.k.body
+
+for.k.body:
+  %k = phi i64 [ 0, %for.j.header ], [ %k.inc, %for.k.inc ]
+  %k.inc = add i64 %k, 1
+  %k.2 = mul i64 %k, 2
+  %d.index = getelementptr [256 x [256 x [256 x float]]], ptr @D, i64 0, i64 %i.inc, i64 %j.inc, i64 %k.2
+  %e.index = getelementptr [256 x [256 x [256 x float]]], ptr @E, i64 0, i64 %i, i64 %j, i64 %k
+  %d.load = load float, ptr %d.index
+  store float %d.load, ptr %e.index
+  %cond = freeze i1 undef
+  br i1 %cond, label %if.then, label %for.k.inc
+
+if.then:
+  %d.index2 = getelementptr [256 x [256 x [256 x float]]], ptr @D, i64 0, i64 %i, i64 %j, i64 %k.inc
+  store float 1.0, ptr %d.index2
+  br label %for.k.inc
+
+for.k.inc:
+  %cmp.k = icmp eq i64 %k.inc, 128
+  br i1 %cmp.k, label %for.j.inc, label %for.k.body
+
+for.j.inc:
+  %cmp.j = icmp eq i64 %j.inc, 255
+  br i1 %cmp.j, label %for.i.inc, label %for.j.header
+
+for.i.inc:
+  %cmp.i = icmp eq i64 %i.inc, 255
+  br i1 %cmp.i, label %exit, label %for.i.header
+
+exit:
+  ret void
+}