diff --git a/mlir/include/mlir/Conversion/Passes.td b/mlir/include/mlir/Conversion/Passes.td
--- a/mlir/include/mlir/Conversion/Passes.td
+++ b/mlir/include/mlir/Conversion/Passes.td
@@ -122,7 +122,11 @@
     Option<"emulateNon32BitScalarTypes", "emulate-non-32-bit-scalar-types",
            "bool", /*default=*/"true",
            "Emulate non-32-bit scalar types with 32-bit ones if "
-           "missing native support">
+           "missing native support">,
+    Option<"enableFastMath", "enable-fast-math",
+           "bool", /*default=*/"false",
+           "Enable fast math mode (assuming no NaN and infinity for floating "
+           "point values) when performing conversion">
   ];
 }
 
diff --git a/mlir/include/mlir/Dialect/SPIRV/Transforms/SPIRVConversion.h b/mlir/include/mlir/Dialect/SPIRV/Transforms/SPIRVConversion.h
--- a/mlir/include/mlir/Dialect/SPIRV/Transforms/SPIRVConversion.h
+++ b/mlir/include/mlir/Dialect/SPIRV/Transforms/SPIRVConversion.h
@@ -26,6 +26,9 @@
 //===----------------------------------------------------------------------===//
 
 struct SPIRVConversionOptions {
+  /// The number of bits to store a boolean value.
+  unsigned boolNumBits{8};
+
   /// Whether to emulate non-32-bit scalar types with 32-bit scalar types if
   /// no native support.
   ///
@@ -45,9 +48,10 @@
   /// Use 64-bit integers to convert index types.
   bool use64bitIndex{false};
 
-  /// The number of bits to store a boolean value. It is eight bits by
-  /// default.
-  unsigned boolNumBits{8};
+  /// Whether to enable fast math mode during conversion. If true, various
+  /// patterns would assume no NaN/infinity numbers as inputs, and thus there
+  /// will be no special guards emitted to check and handle such cases.
+  bool enableFastMathMode{false};
 };
 
 /// Type conversion from builtin types to SPIR-V types for shader interface.
diff --git a/mlir/lib/Conversion/ArithmeticToSPIRV/ArithmeticToSPIRV.cpp b/mlir/lib/Conversion/ArithmeticToSPIRV/ArithmeticToSPIRV.cpp
--- a/mlir/lib/Conversion/ArithmeticToSPIRV/ArithmeticToSPIRV.cpp
+++ b/mlir/lib/Conversion/ArithmeticToSPIRV/ArithmeticToSPIRV.cpp
@@ -219,6 +219,16 @@
                   ConversionPatternRewriter &rewriter) const override;
 };
 
+/// Converts arith.maxf to spv.GL.FMax.
+template <typename Op, typename SPIRVOp>
+class MinMaxFOpPattern final : public OpConversionPattern<Op> {
+public:
+  using OpConversionPattern<Op>::OpConversionPattern;
+  LogicalResult
+  matchAndRewrite(Op op, typename Op::Adaptor adaptor,
+                  ConversionPatternRewriter &rewriter) const override;
+};
+
 } // namespace
 
 //===----------------------------------------------------------------------===//
@@ -839,13 +849,25 @@
     return failure();
 
   Location loc = op.getLoc();
+  auto *converter = getTypeConverter<SPIRVTypeConverter>();
 
-  Value lhsIsNan = rewriter.create<spirv::IsNanOp>(loc, adaptor.getLhs());
-  Value rhsIsNan = rewriter.create<spirv::IsNanOp>(loc, adaptor.getRhs());
+  Value replace;
+  if (converter->getOptions().enableFastMathMode) {
+    if (op.getPredicate() == arith::CmpFPredicate::ORD) {
+      // Ordered comparsion checks if neither operand is NaN.
+      replace = spirv::ConstantOp::getOne(op.getType(), loc, rewriter);
+    } else {
+      // Unordered comparsion checks if either operand is NaN.
+      replace = spirv::ConstantOp::getZero(op.getType(), loc, rewriter);
+    }
+  } else {
+    Value lhsIsNan = rewriter.create<spirv::IsNanOp>(loc, adaptor.getLhs());
+    Value rhsIsNan = rewriter.create<spirv::IsNanOp>(loc, adaptor.getRhs());
 
-  Value replace = rewriter.create<spirv::LogicalOrOp>(loc, lhsIsNan, rhsIsNan);
-  if (op.getPredicate() == arith::CmpFPredicate::ORD)
-    replace = rewriter.create<spirv::LogicalNotOp>(loc, replace);
+    replace = rewriter.create<spirv::LogicalOrOp>(loc, lhsIsNan, rhsIsNan);
+    if (op.getPredicate() == arith::CmpFPredicate::ORD)
+      replace = rewriter.create<spirv::LogicalNotOp>(loc, replace);
+  }
 
   rewriter.replaceOp(op, replace);
   return success();
@@ -889,6 +911,45 @@
   return success();
 }
 
+//===----------------------------------------------------------------------===//
+// MaxFOpPattern
+//===----------------------------------------------------------------------===//
+
+template <typename Op, typename SPIRVOp>
+LogicalResult MinMaxFOpPattern<Op, SPIRVOp>::matchAndRewrite(
+    Op op, typename Op::Adaptor adaptor,
+    ConversionPatternRewriter &rewriter) const {
+  auto *converter = this->template getTypeConverter<SPIRVTypeConverter>();
+  auto dstType = converter->convertType(op.getType());
+  if (!dstType)
+    return failure();
+
+  // arith.maxf/minf:
+  //   "if one of the arguments is NaN, then the result is also NaN."
+  // spv.GL.FMax/FMin:
+  //   "which operand is the result is undefined if one of the operands
+  //   is a NaN."
+
+  Location loc = op.getLoc();
+  Value cmpF = rewriter.create<SPIRVOp>(loc, dstType, adaptor.getOperands());
+
+  if (converter->getOptions().enableFastMathMode) {
+    rewriter.replaceOp(op, cmpF);
+    return success();
+  }
+
+  Value lhsIsNan = rewriter.create<spirv::IsNanOp>(loc, adaptor.getLhs());
+  Value rhsIsNan = rewriter.create<spirv::IsNanOp>(loc, adaptor.getRhs());
+
+  Value select1 = rewriter.create<spirv::SelectOp>(loc, dstType, lhsIsNan,
+                                                   adaptor.getLhs(), cmpF);
+  Value select2 = rewriter.create<spirv::SelectOp>(loc, dstType, rhsIsNan,
+                                                   adaptor.getRhs(), select1);
+
+  rewriter.replaceOp(op, select2);
+  return success();
+}
+
 //===----------------------------------------------------------------------===//
 // Pattern Population
 //===----------------------------------------------------------------------===//
@@ -932,10 +993,10 @@
     CmpFOpNanNonePattern, CmpFOpPattern,
     AddICarryOpPattern, SelectOpPattern,
 
-    spirv::ElementwiseOpPattern<arith::MaxFOp, spirv::GLFMaxOp>,
+    MinMaxFOpPattern<arith::MaxFOp, spirv::GLFMaxOp>,
+    MinMaxFOpPattern<arith::MinFOp, spirv::GLFMinOp>,
     spirv::ElementwiseOpPattern<arith::MaxSIOp, spirv::GLSMaxOp>,
     spirv::ElementwiseOpPattern<arith::MaxUIOp, spirv::GLUMaxOp>,
-    spirv::ElementwiseOpPattern<arith::MinFOp, spirv::GLFMinOp>,
     spirv::ElementwiseOpPattern<arith::MinSIOp, spirv::GLSMinOp>,
     spirv::ElementwiseOpPattern<arith::MinUIOp, spirv::GLUMinOp>
   >(typeConverter, patterns.getContext());
@@ -961,6 +1022,7 @@
 
     SPIRVConversionOptions options;
     options.emulateNon32BitScalarTypes = this->emulateNon32BitScalarTypes;
+    options.enableFastMathMode = this->enableFastMath;
     SPIRVTypeConverter typeConverter(targetAttr, options);
 
     // Use UnrealizedConversionCast as the bridge so that we don't need to pull
diff --git a/mlir/test/Conversion/ArithmeticToSPIRV/arithmetic-to-spirv.mlir b/mlir/test/Conversion/ArithmeticToSPIRV/arithmetic-to-spirv.mlir
--- a/mlir/test/Conversion/ArithmeticToSPIRV/arithmetic-to-spirv.mlir
+++ b/mlir/test/Conversion/ArithmeticToSPIRV/arithmetic-to-spirv.mlir
@@ -1093,13 +1093,35 @@
   %3 = arith.divf %lhs, %rhs: f32
   // CHECK: spv.FRem %{{.*}}, %{{.*}}: f32
   %4 = arith.remf %lhs, %rhs: f32
-  // CHECK: spv.GL.FMax %{{.*}}, %{{.*}}: f32
-  %5 = arith.maxf %lhs, %rhs: f32
-  // CHECK: spv.GL.FMin %{{.*}}, %{{.*}}: f32
-  %6 = arith.minf %lhs, %rhs: f32
   return
 }
 
+// CHECK-LABEL: @float32_minf_scalar
+// CHECK-SAME: %[[LHS:.+]]: f32, %[[RHS:.+]]: f32
+func.func @float32_minf_scalar(%arg0 : f32, %arg1 : f32) -> f32 {
+  // CHECK: %[[MIN:.+]] = spv.GL.FMin %arg0, %arg1 : f32
+  // CHECK: %[[LHS_NAN:.+]] = spv.IsNan %[[LHS]] : f32
+  // CHECK: %[[RHS_NAN:.+]] = spv.IsNan %[[RHS]] : f32
+  // CHECK: %[[SELECT1:.+]] = spv.Select %[[LHS_NAN]], %[[LHS]], %[[MIN]]
+  // CHECK: %[[SELECT2:.+]] = spv.Select %[[RHS_NAN]], %[[RHS]], %[[SELECT1]]
+  %0 = arith.minf %arg0, %arg1 : f32
+  // CHECK: return %[[SELECT2]]
+  return %0: f32
+}
+
+// CHECK-LABEL: @float32_maxf_scalar
+// CHECK-SAME: %[[LHS:.+]]: f32, %[[RHS:.+]]: f32
+func.func @float32_maxf_scalar(%arg0 : f32, %arg1 : f32) -> f32 {
+  // CHECK: %[[MAX:.+]] = spv.GL.FMax %arg0, %arg1 : f32
+  // CHECK: %[[LHS_NAN:.+]] = spv.IsNan %[[LHS]] : f32
+  // CHECK: %[[RHS_NAN:.+]] = spv.IsNan %[[RHS]] : f32
+  // CHECK: %[[SELECT1:.+]] = spv.Select %[[LHS_NAN]], %[[LHS]], %[[MAX]]
+  // CHECK: %[[SELECT2:.+]] = spv.Select %[[RHS_NAN]], %[[RHS]], %[[SELECT1]]
+  %0 = arith.maxf %arg0, %arg1 : f32
+  // CHECK: return %[[SELECT2]]
+  return %0: f32
+}
+
 // Check int vector types.
 // CHECK-LABEL: @int_vector234
 func.func @int_vector234(%arg0: vector<2xi8>, %arg1: vector<4xi64>) {
diff --git a/mlir/test/Conversion/ArithmeticToSPIRV/fast-math.mlir b/mlir/test/Conversion/ArithmeticToSPIRV/fast-math.mlir
new file mode 100644
--- /dev/null
+++ b/mlir/test/Conversion/ArithmeticToSPIRV/fast-math.mlir
@@ -0,0 +1,51 @@
+// RUN: mlir-opt -split-input-file -convert-arith-to-spirv=enable-fast-math -verify-diagnostics %s | FileCheck %s
+
+module attributes {
+  spv.target_env = #spv.target_env<#spv.vce<v1.0, [], []>, #spv.resource_limits<>>
+} {
+
+// CHECK-LABEL: @cmpf_ordered
+// CHECK-SAME: %[[LHS:.+]]: f32, %[[RHS:.+]]: f32
+func.func @cmpf_ordered(%arg0 : f32, %arg1 : f32) -> i1 {
+  // CHECK: %[[T:.+]] = spv.Constant true
+  %0 = arith.cmpf ord, %arg0, %arg1 : f32
+  // CHECK: return %[[T]]
+  return %0: i1
+}
+
+// CHECK-LABEL: @cmpf_unordered
+// CHECK-SAME: %[[LHS:.+]]: f32, %[[RHS:.+]]: f32
+func.func @cmpf_unordered(%arg0 : f32, %arg1 : f32) -> i1 {
+  // CHECK: %[[F:.+]] = spv.Constant false
+  %0 = arith.cmpf uno, %arg0, %arg1 : f32
+  // CHECK: return %[[F]]
+  return %0: i1
+}
+
+} // end module
+
+// -----
+
+module attributes {
+  spv.target_env = #spv.target_env<#spv.vce<v1.0, [Shader], []>, #spv.resource_limits<>>
+} {
+
+// CHECK-LABEL: @minf
+// CHECK-SAME: %[[LHS:.+]]: f32, %[[RHS:.+]]: f32
+func.func @minf(%arg0 : f32, %arg1 : f32) -> f32 {
+  // CHECK: %[[F:.+]] = spv.GL.FMin %[[LHS]], %[[RHS]]
+  %0 = arith.minf %arg0, %arg1 : f32
+  // CHECK: return %[[F]]
+  return %0: f32
+}
+
+// CHECK-LABEL: @maxf
+// CHECK-SAME: %[[LHS:.+]]: f32, %[[RHS:.+]]: f32
+func.func @maxf(%arg0 : f32, %arg1 : f32) -> f32 {
+  // CHECK: %[[F:.+]] = spv.GL.FMax %[[LHS]], %[[RHS]]
+  %0 = arith.maxf %arg0, %arg1 : f32
+  // CHECK: return %[[F]]
+  return %0: f32
+}
+
+} // end module