diff --git a/mlir/include/mlir/Dialect/Linalg/ComprehensiveBufferize/BufferizableOpInterface.td b/mlir/include/mlir/Dialect/Linalg/ComprehensiveBufferize/BufferizableOpInterface.td
--- a/mlir/include/mlir/Dialect/Linalg/ComprehensiveBufferize/BufferizableOpInterface.td
+++ b/mlir/include/mlir/Dialect/Linalg/ComprehensiveBufferize/BufferizableOpInterface.td
@@ -89,6 +89,25 @@
                 });
           }]
       >,
+      InterfaceMethod<
+        /*desc=*/[{
+          Return `true` if the given OpResult must bufferize in-place with its
+          corresponding aliasing OpOperand. Alias sets and inplace attributes
+          will be set up accordingly before making any other bufferization
+          decisions. This method will never be called on OpResults that do not
+          have a tensor type.
+
+          Note: This method may not return `true` if the given OpResult does not
+          have an aliasing OpOperand.
+        }],
+        /*retType=*/"bool",
+        /*methodName=*/"mustBufferizeInPlace",
+        /*args=*/(ins "OpResult":$opResult),
+        /*methodBody=*/"",
+        /*defaultImplementation=*/[{
+          return false;
+        }]
+      >,
       InterfaceMethod<
         /*desc=*/[{
           Return the OpResult that aliases with a given OpOperand when
diff --git a/mlir/lib/Dialect/Linalg/ComprehensiveBufferize/ComprehensiveBufferize.cpp b/mlir/lib/Dialect/Linalg/ComprehensiveBufferize/ComprehensiveBufferize.cpp
--- a/mlir/lib/Dialect/Linalg/ComprehensiveBufferize/ComprehensiveBufferize.cpp
+++ b/mlir/lib/Dialect/Linalg/ComprehensiveBufferize/ComprehensiveBufferize.cpp
@@ -538,18 +538,20 @@
             createAliasInfoEntry(bbArg);
   });
 
-  // The return value of an scf::IfOp aliases with both yield values.
-  rootOp->walk([&](scf::IfOp ifOp) {
-    if (ifOp->getNumResults() > 0) {
-      for (auto it : llvm::zip(ifOp.thenYield().results(),
-                               ifOp.elseYield().results(), ifOp.results())) {
-        aliasInfo.unionSets(std::get<0>(it), std::get<1>(it));
-        aliasInfo.unionSets(std::get<0>(it), std::get<2>(it));
-      }
-
-      // scf::IfOp always bufferizes in-place.
-      for (OpResult opResult : ifOp->getResults())
-        setInPlaceOpResult(opResult, InPlaceSpec::True);
+  // Set up alias sets for OpResults that must bufferize in-place. This should
+  // be done before making any other bufferization decisions.
+  rootOp->walk([&](BufferizableOpInterface bufferizableOp) {
+    for (OpResult opResult : bufferizableOp->getOpResults()) {
+      if (opResult.getType().isa<TensorType>())
+        if (bufferizableOp.mustBufferizeInPlace(opResult)) {
+          SmallVector<OpOperand *> operands =
+              bufferizableOp.getAliasingOpOperand(opResult);
+          assert(!operands.empty() &&
+                 "expected that OpResult has aliasing OpOperand");
+          for (OpOperand *operand : operands)
+            aliasInfo.unionSets(operand->get(), opResult);
+          setInPlaceOpResult(opResult, InPlaceSpec::True);
+        }
     }
   });
 }
@@ -2753,6 +2755,12 @@
     return true;
   }
 
+  bool mustBufferizeInPlace(Operation *op, OpResult opResult) const {
+    // IfOp results always bufferize in-place. Since they have no OpOperands,
+    // they are mostly ignored by the analysis once alias sets are set up.
+    return true;
+  }
+
   LogicalResult bufferize(Operation *op, OpBuilder &b,
                           BlockAndValueMapping &bvm,
                           BufferizationAliasInfo &aliasInfo,