diff --git a/paddle/fluid/operators/dist_op.cc b/paddle/fluid/operators/dist_op.cc
index 3a53f1365567f..10750574c4573 100644
--- a/paddle/fluid/operators/dist_op.cc
+++ b/paddle/fluid/operators/dist_op.cc
@@ -12,10 +12,13 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-#include "paddle/fluid/operators/dist_op.h"
 #include <string>
 #include <vector>
+#include "paddle/fluid/framework/infershape_utils.h"
 #include "paddle/fluid/framework/op_registry.h"
+#include "paddle/phi/core/infermeta_utils.h"
+#include "paddle/phi/infermeta/binary.h"
+
 namespace paddle {
 namespace operators {
 
@@ -121,13 +124,11 @@ class DistGradOpMaker : public framework::SingleGradOpMaker<T> {
 }  // namespace paddle
 
 namespace ops = paddle::operators;
+DELCARE_INFER_SHAPE_FUNCTOR(dist, DistInferShapeFunctor,
+                            PT_INFER_META(phi::DistInferMeta));
+
 REGISTER_OPERATOR(dist, ops::DistOp, ops::DistOpMaker,
                   ops::DistGradOpMaker<paddle::framework::OpDesc>,
-                  ops::DistGradOpMaker<paddle::imperative::OpBase>);
+                  ops::DistGradOpMaker<paddle::imperative::OpBase>,
+                  DistInferShapeFunctor);
 REGISTER_OPERATOR(dist_grad, ops::DistOpGrad);
-REGISTER_OP_CPU_KERNEL(
-    dist, ops::DistKernel<paddle::platform::CPUDeviceContext, float>,
-    ops::DistKernel<paddle::platform::CPUDeviceContext, double>);
-REGISTER_OP_CPU_KERNEL(
-    dist_grad, ops::DistGradKernel<paddle::platform::CPUDeviceContext, float>,
-    ops::DistGradKernel<paddle::platform::CPUDeviceContext, double>)
diff --git a/paddle/fluid/operators/dist_op.h b/paddle/fluid/operators/dist_op.h
deleted file mode 100644
index dfd7e29a8d010..0000000000000
--- a/paddle/fluid/operators/dist_op.h
+++ /dev/null
@@ -1,304 +0,0 @@
-// Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     http://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-#pragma once
-
-#include <math.h>
-#include <algorithm>
-#include <vector>
-#include "paddle/fluid/framework/eigen.h"
-#include "paddle/fluid/framework/op_registry.h"
-#include "paddle/phi/kernels/funcs/math_function.h"
-
-namespace paddle {
-namespace operators {
-
-template <typename T, size_t D, int MajorType = Eigen::RowMajor,
-          typename IndexType = Eigen::DenseIndex>
-using EigenTensor = framework::EigenTensor<T, D, MajorType, IndexType>;
-using framework::Tensor;
-
-template <int Rank>
-static void GetBraodcastDims(const framework::DDim& x_dims,
-                             const framework::DDim& y_dims,
-                             Eigen::DSizes<int, Rank>* x_bcast_dims,
-                             Eigen::DSizes<int, Rank>* y_bcast_dims) {
-  int bcast_dims_remainder = 0;
-  for (int i = 0; i < x_dims.size(); ++i) {
-    if (x_dims[i] >= y_dims[i]) {
-      (*x_bcast_dims)[i] = 1;
-      (*y_bcast_dims)[i] = x_dims[i] / y_dims[i];
-      bcast_dims_remainder += x_dims[i] % y_dims[i];
-    } else {
-      (*y_bcast_dims)[i] = 1;
-      (*x_bcast_dims)[i] = y_dims[i] / x_dims[i];
-      bcast_dims_remainder += y_dims[i] % x_dims[i];
-    }
-  }
-  PADDLE_ENFORCE_EQ(bcast_dims_remainder, 0,
-                    platform::errors::PreconditionNotMet(
-                        "The input tensor of Op(dist) could not be broadcast, "
-                        "X's shape is [%s], Y's shape is [%s].",
-                        x_dims, y_dims));
-}
-
-static framework::DDim GetNewDims(const framework::DDim& in_dims, int rank) {
-  std::vector<int64_t> new_dims_vec(rank);
-  if (in_dims.size() < rank) {
-    for (int i = 0; i < rank - in_dims.size(); ++i) {
-      new_dims_vec[i] = 1;
-    }
-    for (int i = 0; i < in_dims.size(); ++i) {
-      new_dims_vec[i + rank - in_dims.size()] = in_dims[i];
-    }
-  } else {
-    new_dims_vec = vectorize(in_dims);
-  }
-  return phi::make_ddim(new_dims_vec);
-}
-
-template <typename DeviceContext, typename T, int Rank>
-static void DistFunction(const framework::ExecutionContext& context) {
-  auto* x = context.Input<Tensor>("X");
-  auto* y = context.Input<Tensor>("Y");
-  auto* out = context.Output<Tensor>("Out");
-  auto p = context.Attr<float>("p");
-  out->mutable_data<T>(context.GetPlace());
-
-  auto x_dims = context.Input<Tensor>("X")->dims();
-  auto y_dims = context.Input<Tensor>("Y")->dims();
-
-  // new dims with same size as rank, e.g. (rank=3, (4, 3) => (1, 4, 3))
-  framework::DDim x_new_dims = GetNewDims(x_dims, Rank);
-  framework::DDim y_new_dims = GetNewDims(y_dims, Rank);
-
-  auto x_t = EigenTensor<T, Rank>::From(*x, x_new_dims);
-  auto y_t = EigenTensor<T, Rank>::From(*y, y_new_dims);
-  auto out_t = EigenTensor<T, 1>::From(*out);
-  auto& place =
-      *context.template device_context<DeviceContext>().eigen_device();
-
-  Eigen::DSizes<int, Rank> x_bcast_dims;
-  Eigen::DSizes<int, Rank> y_bcast_dims;
-  GetBraodcastDims<Rank>(x_new_dims, y_new_dims, &x_bcast_dims, &y_bcast_dims);
-  // p=0 means number of non-zero elements of (x-y)
-  // p=inf means the maximum of |x-y|
-  // p=-inf means the minimum of |x-y|
-  // otherwise, Lp-norm = pow(sum(pow(|x-y|, p)), 1/p)
-  if (p == 0) {
-    out_t.device(place) =
-        (x_t.broadcast(x_bcast_dims) != y_t.broadcast(y_bcast_dims))
-            .template cast<T>()
-            .sum();
-  } else if (p == INFINITY) {
-    out_t.device(place) =
-        (x_t.broadcast(x_bcast_dims) - y_t.broadcast(y_bcast_dims))
-            .abs()
-            .maximum();
-  } else if (p == -INFINITY) {
-    out_t.device(place) =
-        (x_t.broadcast(x_bcast_dims) - y_t.broadcast(y_bcast_dims))
-            .abs()
-            .minimum();
-  } else {
-    out_t.device(place) =
-        (x_t.broadcast(x_bcast_dims) - y_t.broadcast(y_bcast_dims))
-            .abs()
-            .pow(p)
-            .sum()
-            .pow(1.0 / p);
-  }
-}
-
-template <typename DeviceContext, typename T, int Rank>
-static void DistGradFunction(const framework::ExecutionContext& context) {
-  auto* x = context.Input<Tensor>("X");
-  auto* y = context.Input<Tensor>("Y");
-  auto* out = context.Input<Tensor>("Out");
-  auto p = context.Attr<float>("p");
-
-  auto x_grad = context.Output<Tensor>(framework::GradVarName("X"));
-  auto y_grad = context.Output<Tensor>(framework::GradVarName("Y"));
-  auto out_grad = context.Input<Tensor>(framework::GradVarName("Out"));
-
-  auto x_dims = context.Input<Tensor>("X")->dims();
-  auto y_dims = context.Input<Tensor>("Y")->dims();
-  auto out_dims = context.Input<Tensor>("Out")->dims();
-
-  framework::DDim x_new_dims = GetNewDims(x_dims, Rank);
-  framework::DDim y_new_dims = GetNewDims(y_dims, Rank);
-  framework::DDim out_new_dims = GetNewDims(out_dims, Rank);
-  auto x_t = EigenTensor<T, Rank>::From(*x, x_new_dims);
-  auto y_t = EigenTensor<T, Rank>::From(*y, y_new_dims);
-  auto out_t = EigenTensor<T, Rank>::From(*out, out_new_dims);
-
-  Eigen::DSizes<int, Rank> x_bcast_dims;
-  Eigen::DSizes<int, Rank> y_bcast_dims;
-  Eigen::DSizes<int, Rank> out_bcast_dims;
-
-  GetBraodcastDims<Rank>(x_new_dims, y_new_dims, &x_bcast_dims, &y_bcast_dims);
-  std::vector<int64_t> new_dims_vec(Rank);
-  for (int i = 0; i < Rank; ++i) {
-    new_dims_vec[i] = std::max(x_new_dims[i], y_new_dims[i]);
-    out_bcast_dims[i] = new_dims_vec[i];
-  }
-  framework::DDim new_dims = phi::make_ddim(new_dims_vec);
-
-  auto& place =
-      *context.template device_context<DeviceContext>().eigen_device();
-  auto out_grad_t = EigenTensor<T, Rank>::From(*out_grad, out_new_dims);
-  framework::Tensor grad;
-  grad.mutable_data<T>(new_dims, context.GetPlace());
-  auto grad_t = EigenTensor<T, Rank>::From(grad);
-
-  auto x_minux_y = x_t.broadcast(x_bcast_dims) - y_t.broadcast(y_bcast_dims);
-  auto x_minux_y_abs = x_minux_y.abs();
-  auto sign =
-      (x_minux_y > static_cast<T>(0)).template cast<T>() * static_cast<T>(1.0) +
-      (x_minux_y < static_cast<T>(0)).template cast<T>() * static_cast<T>(-1.0);
-  T epsilon = static_cast<T>(1.0e-10f);
-
-  // 1: Lp-norm(z), z = x-y, compute dz
-  if (p == 0) {
-    phi::funcs::SetConstant<DeviceContext, T> set_zero;
-    auto& dev_ctx = context.template device_context<DeviceContext>();
-    set_zero(dev_ctx, &grad, static_cast<T>(0));
-  } else if (p == INFINITY || p == -INFINITY) {
-    // p=inf or -inf, Lp-norm = |z_i|, the j-th element of dz tends to 0 if
-    // j!=i, or equals to sign(z_i) * dout if j=i.
-    if (platform::is_cpu_place(context.GetPlace())) {
-      grad_t.device(place) = (x_minux_y_abs == out_t.broadcast(out_bcast_dims))
-                                 .template cast<T>() *
-                             sign.eval() * out_grad_t.broadcast(out_bcast_dims);
-    } else {
-      grad_t.device(place) = (x_minux_y_abs == out_t.broadcast(out_bcast_dims))
-                                 .template cast<T>() *
-                             sign * out_grad_t.broadcast(out_bcast_dims);
-    }
-  } else {
-    // dz = pow(abs(x-y)/out, p-1) * sign(x-y) * dout
-    if (platform::is_cpu_place(context.GetPlace())) {
-      grad_t.device(place) =
-          (x_minux_y_abs / (out_t + epsilon).broadcast(out_bcast_dims))
-              .pow(p - 1) *
-          sign.eval() * out_grad_t.broadcast(out_bcast_dims);
-    } else {
-      grad_t.device(place) =
-          (x_minux_y_abs / (out_t + epsilon).broadcast(out_bcast_dims))
-              .pow(p - 1) *
-          sign * out_grad_t.broadcast(out_bcast_dims);
-    }
-  }
-
-  Eigen::DSizes<int, Rank * 2> x_reshape_dims;
-  Eigen::DSizes<int, Rank * 2> y_reshape_dims;
-  Eigen::DSizes<int, Rank> reduce_dims;
-  for (int i = 0; i < x_new_dims.size(); ++i) {
-    x_reshape_dims[2 * i] = x_bcast_dims[i];
-    x_reshape_dims[2 * i + 1] = x_new_dims[i];
-    y_reshape_dims[2 * i] = y_bcast_dims[i];
-    y_reshape_dims[2 * i + 1] = y_new_dims[i];
-    reduce_dims[i] = 2 * i;
-  }
-
-  // 2: if x or y is broadcasted in forward function,
-  // the grad need to be sum along the broadcasted dimensions
-  if (x_grad) {
-    x_grad->mutable_data<T>(context.GetPlace());
-    auto x_grad_t = EigenTensor<T, Rank>::From(*x_grad, x_new_dims);
-    x_grad_t.device(place) = grad_t.reshape(x_reshape_dims)
-                                 .sum(reduce_dims)
-                                 .reshape(x_grad_t.dimensions());
-  }
-  if (y_grad) {
-    y_grad->mutable_data<T>(context.GetPlace());
-    auto y_grad_t = EigenTensor<T, Rank>::From(*y_grad, y_new_dims);
-    y_grad_t.device(place) = -grad_t.reshape(y_reshape_dims)
-                                  .sum(reduce_dims)
-                                  .reshape(y_grad_t.dimensions());
-  }
-}
-
-template <typename DeviceContext, typename T>
-class DistKernel : public framework::OpKernel<T> {
- public:
-  void Compute(const framework::ExecutionContext& context) const override {
-    auto x_rank = context.Input<Tensor>("X")->dims().size();
-    auto y_rank = context.Input<Tensor>("Y")->dims().size();
-    auto rank = std::max(x_rank, y_rank);
-    PADDLE_ENFORCE_LE(rank, 6,
-                      platform::errors::Unimplemented(
-                          "Op(dist) only support tensors with no more than 6 "
-                          "dimensions, but X's rank is %d, Y's rank is %d.",
-                          x_rank, y_rank));
-    switch (rank) {
-      case 1:
-        DistFunction<DeviceContext, T, 1>(context);
-        break;
-      case 2:
-        DistFunction<DeviceContext, T, 2>(context);
-        break;
-      case 3:
-        DistFunction<DeviceContext, T, 3>(context);
-        break;
-      case 4:
-        DistFunction<DeviceContext, T, 4>(context);
-        break;
-      case 5:
-        DistFunction<DeviceContext, T, 5>(context);
-        break;
-      case 6:
-        DistFunction<DeviceContext, T, 6>(context);
-        break;
-    }
-  }
-};
-
-template <typename DeviceContext, typename T>
-class DistGradKernel : public framework::OpKernel<T> {
- public:
-  void Compute(const framework::ExecutionContext& context) const override {
-    auto x_rank = context.Input<Tensor>("X")->dims().size();
-    auto y_rank = context.Input<Tensor>("Y")->dims().size();
-    auto rank = std::max(x_rank, y_rank);
-    PADDLE_ENFORCE_LE(rank, 6,
-                      platform::errors::Unimplemented(
-                          "Op(dist) only support tensors with no more than 6 "
-                          "dimensions, but X's rank is %d, Y's rank is %d.",
-                          x_rank, y_rank));
-    switch (rank) {
-      case 1:
-        DistGradFunction<DeviceContext, T, 1>(context);
-        break;
-      case 2:
-        DistGradFunction<DeviceContext, T, 2>(context);
-        break;
-      case 3:
-        DistGradFunction<DeviceContext, T, 3>(context);
-        break;
-      case 4:
-        DistGradFunction<DeviceContext, T, 4>(context);
-        break;
-      case 5:
-        DistGradFunction<DeviceContext, T, 5>(context);
-        break;
-      case 6:
-        DistGradFunction<DeviceContext, T, 6>(context);
-        break;
-    }
-  }
-};
-
-}  // namespace operators
-}  // namespace paddle
diff --git a/paddle/phi/infermeta/binary.cc b/paddle/phi/infermeta/binary.cc
index 745ddffabbe33..c3c159dfc0a69 100644
--- a/paddle/phi/infermeta/binary.cc
+++ b/paddle/phi/infermeta/binary.cc
@@ -397,6 +397,29 @@ void BCELossInferMeta(const MetaTensor& input,
   out->share_lod(input);
 }
 
+void DistInferMeta(const MetaTensor& x,
+                   const MetaTensor& y,
+                   float p,
+                   MetaTensor* out) {
+  auto x_dims = x.dims();
+  auto y_dims = y.dims();
+
+  PADDLE_ENFORCE_NE(phi::product(x_dims),
+                    0,
+                    phi::errors::InvalidArgument(
+                        "The Input(X) has not been initialized properly. The "
+                        "shape of Input(X) = [%s].",
+                        x_dims));
+  PADDLE_ENFORCE_NE(phi::product(y_dims),
+                    0,
+                    phi::errors::InvalidArgument(
+                        "The Input(Y) has not been initialized properly. The "
+                        "shape of Input(Y) = [%s].",
+                        y_dims));
+  out->set_dims({1});
+  out->set_dtype(x.dtype());
+}
+
 void GatherNdInferMeta(const MetaTensor& x,
                        const MetaTensor& index,
                        MetaTensor* out) {
diff --git a/paddle/phi/infermeta/binary.h b/paddle/phi/infermeta/binary.h
index 2ec744636988f..11db19fc410d0 100644
--- a/paddle/phi/infermeta/binary.h
+++ b/paddle/phi/infermeta/binary.h
@@ -78,6 +78,11 @@ void BCELossInferMeta(const MetaTensor& input,
                       MetaTensor* out,
                       MetaConfig config = MetaConfig());
 
+void DistInferMeta(const MetaTensor& x,
+                   const MetaTensor& y,
+                   float p,
+                   MetaTensor* out);
+
 void GatherNdInferMeta(const MetaTensor& x,
                        const MetaTensor& index,
                        MetaTensor* out);
diff --git a/paddle/phi/kernels/cpu/dist_grad_kernel.cc b/paddle/phi/kernels/cpu/dist_grad_kernel.cc
new file mode 100644
index 0000000000000..2b7f8f98f9473
--- /dev/null
+++ b/paddle/phi/kernels/cpu/dist_grad_kernel.cc
@@ -0,0 +1,22 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "paddle/phi/kernels/dist_grad_kernel.h"
+#include "paddle/phi/kernels/impl/dist_grad_kernel_impl.h"
+
+#include "paddle/phi/backends/cpu/cpu_context.h"
+#include "paddle/phi/core/kernel_registry.h"
+
+PD_REGISTER_KERNEL(
+    dist_grad, CPU, ALL_LAYOUT, phi::DistGradKernel, float, double) {}
diff --git a/paddle/phi/kernels/cpu/dist_kernel.cc b/paddle/phi/kernels/cpu/dist_kernel.cc
new file mode 100644
index 0000000000000..ccf3d4be83230
--- /dev/null
+++ b/paddle/phi/kernels/cpu/dist_kernel.cc
@@ -0,0 +1,21 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "paddle/phi/kernels/dist_kernel.h"
+#include "paddle/phi/kernels/impl/dist_kernel_impl.h"
+
+#include "paddle/phi/backends/cpu/cpu_context.h"
+#include "paddle/phi/core/kernel_registry.h"
+
+PD_REGISTER_KERNEL(dist, CPU, ALL_LAYOUT, phi::DistKernel, float, double) {}
diff --git a/paddle/phi/kernels/dist_grad_kernel.h b/paddle/phi/kernels/dist_grad_kernel.h
new file mode 100644
index 0000000000000..1f8d7ff21f2fe
--- /dev/null
+++ b/paddle/phi/kernels/dist_grad_kernel.h
@@ -0,0 +1,31 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#pragma once
+
+#include "paddle/phi/core/dense_tensor.h"
+
+namespace phi {
+
+template <typename T, typename Context>
+void DistGradKernel(const Context& dev_ctx,
+                    const DenseTensor& x,
+                    const DenseTensor& y,
+                    const DenseTensor& out,
+                    const DenseTensor& out_grad,
+                    float p,
+                    DenseTensor* x_grad,
+                    DenseTensor* y_grad);
+
+}  // namespace phi
diff --git a/paddle/phi/kernels/dist_kernel.h b/paddle/phi/kernels/dist_kernel.h
new file mode 100644
index 0000000000000..6cb3d6e0e8bef
--- /dev/null
+++ b/paddle/phi/kernels/dist_kernel.h
@@ -0,0 +1,28 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#pragma once
+
+#include "paddle/phi/core/dense_tensor.h"
+
+namespace phi {
+
+template <typename T, typename Context>
+void DistKernel(const Context& dev_ctx,
+                const DenseTensor& x,
+                const DenseTensor& y,
+                float p,
+                DenseTensor* out);
+
+}  // namespace phi
diff --git a/paddle/phi/kernels/gpu/dist_grad_kernel.cu b/paddle/phi/kernels/gpu/dist_grad_kernel.cu
new file mode 100644
index 0000000000000..c458f8cce3e0a
--- /dev/null
+++ b/paddle/phi/kernels/gpu/dist_grad_kernel.cu
@@ -0,0 +1,26 @@
+/* Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License. */
+
+#include "paddle/phi/kernels/dist_grad_kernel.h"
+#include "paddle/phi/kernels/impl/dist_grad_kernel_impl.h"
+
+#include "paddle/phi/backends/gpu/gpu_context.h"
+#include "paddle/phi/core/kernel_registry.h"
+
+#ifdef PADDLE_WITH_HIP
+PD_REGISTER_KERNEL(dist_grad, GPU, ALL_LAYOUT, phi::DistGradKernel, float) {}
+#else
+PD_REGISTER_KERNEL(
+    dist_grad, GPU, ALL_LAYOUT, phi::DistGradKernel, float, double) {}
+#endif
diff --git a/paddle/fluid/operators/dist_op.cu b/paddle/phi/kernels/gpu/dist_kernel.cu
similarity index 51%
rename from paddle/fluid/operators/dist_op.cu
rename to paddle/phi/kernels/gpu/dist_kernel.cu
index 90674969e283f..87e75e02754a8 100644
--- a/paddle/fluid/operators/dist_op.cu
+++ b/paddle/phi/kernels/gpu/dist_kernel.cu
@@ -1,4 +1,4 @@
-// Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
 //
 // Licensed under the Apache License, Version 2.0 (the "License");
 // you may not use this file except in compliance with the License.
@@ -12,21 +12,16 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-#include "paddle/fluid/operators/dist_op.h"
+#include "paddle/phi/kernels/dist_kernel.h"
+#include "paddle/phi/kernels/impl/dist_kernel_impl.h"
+
+#include "paddle/phi/backends/gpu/gpu_context.h"
+#include "paddle/phi/core/kernel_registry.h"
 
-namespace ops = paddle::operators;
 #ifdef PADDLE_WITH_HIP
 // Eigen3/unsupported/Eigen/CXX11/src/Tensor/TensorReductionGpu.h:922
 // do not support double in HIPCC platform (Eigen3 to be fixed)
-REGISTER_OP_CUDA_KERNEL(
-    dist, ops::DistKernel<paddle::platform::CUDADeviceContext, float>);
-REGISTER_OP_CUDA_KERNEL(
-    dist_grad, ops::DistGradKernel<paddle::platform::CUDADeviceContext, float>);
+PD_REGISTER_KERNEL(dist, GPU, ALL_LAYOUT, phi::DistKernel, float) {}
 #else
-REGISTER_OP_CUDA_KERNEL(
-    dist, ops::DistKernel<paddle::platform::CUDADeviceContext, float>,
-    ops::DistKernel<paddle::platform::CUDADeviceContext, double>);
-REGISTER_OP_CUDA_KERNEL(
-    dist_grad, ops::DistGradKernel<paddle::platform::CUDADeviceContext, float>,
-    ops::DistGradKernel<paddle::platform::CUDADeviceContext, double>);
+PD_REGISTER_KERNEL(dist, GPU, ALL_LAYOUT, phi::DistKernel, float, double) {}
 #endif
diff --git a/paddle/phi/kernels/impl/dist_grad_kernel_impl.h b/paddle/phi/kernels/impl/dist_grad_kernel_impl.h
new file mode 100644
index 0000000000000..fc118a832dc9f
--- /dev/null
+++ b/paddle/phi/kernels/impl/dist_grad_kernel_impl.h
@@ -0,0 +1,223 @@
+/* Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License. */
+
+#pragma once
+
+#include "paddle/phi/core/dense_tensor.h"
+#include "paddle/phi/kernels/funcs/eigen/common.h"
+#include "paddle/phi/kernels/funcs/math_function.h"
+
+namespace phi {
+
+template <typename T,
+          size_t D,
+          int MajorType = Eigen::RowMajor,
+          typename IndexType = Eigen::DenseIndex>
+using ETensor = phi::EigenTensor<T, D, MajorType, IndexType>;
+
+template <int Rank>
+static void GetBraodcastDims(const phi::DDim& x_dims,
+                             const phi::DDim& y_dims,
+                             Eigen::DSizes<int, Rank>* x_bcast_dims,
+                             Eigen::DSizes<int, Rank>* y_bcast_dims) {
+  int bcast_dims_remainder = 0;
+  for (int i = 0; i < x_dims.size(); ++i) {
+    if (x_dims[i] >= y_dims[i]) {
+      (*x_bcast_dims)[i] = 1;
+      (*y_bcast_dims)[i] = x_dims[i] / y_dims[i];
+      bcast_dims_remainder += x_dims[i] % y_dims[i];
+    } else {
+      (*y_bcast_dims)[i] = 1;
+      (*x_bcast_dims)[i] = y_dims[i] / x_dims[i];
+      bcast_dims_remainder += y_dims[i] % x_dims[i];
+    }
+  }
+  PADDLE_ENFORCE_EQ(bcast_dims_remainder,
+                    0,
+                    phi::errors::PreconditionNotMet(
+                        "The input tensor of Op(dist) could not be broadcast, "
+                        "X's shape is [%s], Y's shape is [%s].",
+                        x_dims,
+                        y_dims));
+}
+
+static phi::DDim GetNewDims(const phi::DDim& in_dims, int rank) {
+  std::vector<int64_t> new_dims_vec(rank);
+  if (in_dims.size() < rank) {
+    for (int i = 0; i < rank - in_dims.size(); ++i) {
+      new_dims_vec[i] = 1;
+    }
+    for (int i = 0; i < in_dims.size(); ++i) {
+      new_dims_vec[i + rank - in_dims.size()] = in_dims[i];
+    }
+  } else {
+    new_dims_vec = vectorize(in_dims);
+  }
+  return phi::make_ddim(new_dims_vec);
+}
+
+template <typename Context, typename T, int Rank>
+static void DistGradFunction(const Context& dev_ctx,
+                             const DenseTensor& x,
+                             const DenseTensor& y,
+                             const DenseTensor& out,
+                             const DenseTensor& out_grad,
+                             float p,
+                             DenseTensor* x_grad,
+                             DenseTensor* y_grad) {
+  auto x_dims = x.dims();
+  auto y_dims = y.dims();
+  auto out_dims = out.dims();
+
+  phi::DDim x_new_dims = GetNewDims(x_dims, Rank);
+  phi::DDim y_new_dims = GetNewDims(y_dims, Rank);
+  phi::DDim out_new_dims = GetNewDims(out_dims, Rank);
+  auto x_t = ETensor<T, Rank>::From(x, x_new_dims);
+  auto y_t = ETensor<T, Rank>::From(y, y_new_dims);
+  auto out_t = ETensor<T, Rank>::From(out, out_new_dims);
+
+  Eigen::DSizes<int, Rank> x_bcast_dims;
+  Eigen::DSizes<int, Rank> y_bcast_dims;
+  Eigen::DSizes<int, Rank> out_bcast_dims;
+
+  GetBraodcastDims<Rank>(x_new_dims, y_new_dims, &x_bcast_dims, &y_bcast_dims);
+  std::vector<int64_t> new_dims_vec(Rank);
+  for (int i = 0; i < Rank; ++i) {
+    new_dims_vec[i] = std::max(x_new_dims[i], y_new_dims[i]);
+    out_bcast_dims[i] = new_dims_vec[i];
+  }
+  phi::DDim new_dims = phi::make_ddim(new_dims_vec);
+
+  auto& place = *dev_ctx.eigen_device();
+  auto out_grad_t = ETensor<T, Rank>::From(out_grad, out_new_dims);
+  DenseTensor grad;
+  grad.Resize(new_dims);
+  dev_ctx.template Alloc<T>(&grad);
+  auto grad_t = ETensor<T, Rank>::From(grad);
+
+  auto x_minux_y = x_t.broadcast(x_bcast_dims) - y_t.broadcast(y_bcast_dims);
+  auto x_minux_y_abs = x_minux_y.abs();
+  auto sign =
+      (x_minux_y > static_cast<T>(0)).template cast<T>() * static_cast<T>(1.0) +
+      (x_minux_y < static_cast<T>(0)).template cast<T>() * static_cast<T>(-1.0);
+  T epsilon = static_cast<T>(1.0e-10f);
+
+  // 1: Lp-norm(z), z = x-y, compute dz
+  if (p == 0) {
+    phi::funcs::SetConstant<Context, T> set_zero;
+    set_zero(dev_ctx, &grad, static_cast<T>(0));
+  } else if (p == INFINITY || p == -INFINITY) {
+    // p=inf or -inf, Lp-norm = |z_i|, the j-th element of dz tends to 0 if
+    // j!=i, or equals to sign(z_i) * dout if j=i.
+    if (paddle::platform::is_cpu_place(dev_ctx.GetPlace())) {
+      grad_t.device(place) = (x_minux_y_abs == out_t.broadcast(out_bcast_dims))
+                                 .template cast<T>() *
+                             sign.eval() * out_grad_t.broadcast(out_bcast_dims);
+    } else {
+      grad_t.device(place) = (x_minux_y_abs == out_t.broadcast(out_bcast_dims))
+                                 .template cast<T>() *
+                             sign * out_grad_t.broadcast(out_bcast_dims);
+    }
+  } else {
+    // dz = pow(abs(x-y)/out, p-1) * sign(x-y) * dout
+    if (paddle::platform::is_cpu_place(dev_ctx.GetPlace())) {
+      grad_t.device(place) =
+          (x_minux_y_abs / (out_t + epsilon).broadcast(out_bcast_dims))
+              .pow(p - 1) *
+          sign.eval() * out_grad_t.broadcast(out_bcast_dims);
+    } else {
+      grad_t.device(place) =
+          (x_minux_y_abs / (out_t + epsilon).broadcast(out_bcast_dims))
+              .pow(p - 1) *
+          sign * out_grad_t.broadcast(out_bcast_dims);
+    }
+  }
+
+  Eigen::DSizes<int, Rank * 2> x_reshape_dims;
+  Eigen::DSizes<int, Rank * 2> y_reshape_dims;
+  Eigen::DSizes<int, Rank> reduce_dims;
+  for (int i = 0; i < x_new_dims.size(); ++i) {
+    x_reshape_dims[2 * i] = x_bcast_dims[i];
+    x_reshape_dims[2 * i + 1] = x_new_dims[i];
+    y_reshape_dims[2 * i] = y_bcast_dims[i];
+    y_reshape_dims[2 * i + 1] = y_new_dims[i];
+    reduce_dims[i] = 2 * i;
+  }
+
+  // 2: if x or y is broadcasted in forward function,
+  // the grad need to be sum along the broadcasted dimensions
+  if (x_grad) {
+    dev_ctx.template Alloc<T>(x_grad);
+    auto x_grad_t = ETensor<T, Rank>::From(*x_grad, x_new_dims);
+    x_grad_t.device(place) = grad_t.reshape(x_reshape_dims)
+                                 .sum(reduce_dims)
+                                 .reshape(x_grad_t.dimensions());
+  }
+  if (y_grad) {
+    dev_ctx.template Alloc<T>(y_grad);
+    auto y_grad_t = ETensor<T, Rank>::From(*y_grad, y_new_dims);
+    y_grad_t.device(place) = -grad_t.reshape(y_reshape_dims)
+                                  .sum(reduce_dims)
+                                  .reshape(y_grad_t.dimensions());
+  }
+}
+
+template <typename T, typename Context>
+void DistGradKernel(const Context& dev_ctx,
+                    const DenseTensor& x,
+                    const DenseTensor& y,
+                    const DenseTensor& out,
+                    const DenseTensor& out_grad,
+                    float p,
+                    DenseTensor* x_grad,
+                    DenseTensor* y_grad) {
+  auto x_rank = x.dims().size();
+  auto y_rank = y.dims().size();
+  auto rank = std::max(x_rank, y_rank);
+  PADDLE_ENFORCE_LE(rank,
+                    6,
+                    phi::errors::Unimplemented(
+                        "Op(dist) only support tensors with no more than 6 "
+                        "dimensions, but X's rank is %d, Y's rank is %d.",
+                        x_rank,
+                        y_rank));
+  switch (rank) {
+    case 1:
+      DistGradFunction<Context, T, 1>(
+          dev_ctx, x, y, out, out_grad, p, x_grad, y_grad);
+      break;
+    case 2:
+      DistGradFunction<Context, T, 2>(
+          dev_ctx, x, y, out, out_grad, p, x_grad, y_grad);
+      break;
+    case 3:
+      DistGradFunction<Context, T, 3>(
+          dev_ctx, x, y, out, out_grad, p, x_grad, y_grad);
+      break;
+    case 4:
+      DistGradFunction<Context, T, 4>(
+          dev_ctx, x, y, out, out_grad, p, x_grad, y_grad);
+      break;
+    case 5:
+      DistGradFunction<Context, T, 5>(
+          dev_ctx, x, y, out, out_grad, p, x_grad, y_grad);
+      break;
+    case 6:
+      DistGradFunction<Context, T, 6>(
+          dev_ctx, x, y, out, out_grad, p, x_grad, y_grad);
+      break;
+  }
+}
+
+}  // namespace phi
diff --git a/paddle/phi/kernels/impl/dist_kernel_impl.h b/paddle/phi/kernels/impl/dist_kernel_impl.h
new file mode 100644
index 0000000000000..397fc1b922433
--- /dev/null
+++ b/paddle/phi/kernels/impl/dist_kernel_impl.h
@@ -0,0 +1,164 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#pragma once
+
+#include <math.h>
+#include <algorithm>
+#include <vector>
+#include "paddle/phi/core/dense_tensor.h"
+#include "paddle/phi/kernels/funcs/eigen/common.h"
+#include "paddle/phi/kernels/funcs/math_function.h"
+
+namespace phi {
+
+template <typename T,
+          size_t D,
+          int MajorType = Eigen::RowMajor,
+          typename IndexType = Eigen::DenseIndex>
+using ETensor = phi::EigenTensor<T, D, MajorType, IndexType>;
+
+template <int Rank>
+static void GetBraodcastDims(const phi::DDim& x_dims,
+                             const phi::DDim& y_dims,
+                             Eigen::DSizes<int, Rank>* x_bcast_dims,
+                             Eigen::DSizes<int, Rank>* y_bcast_dims) {
+  int bcast_dims_remainder = 0;
+  for (int i = 0; i < x_dims.size(); ++i) {
+    if (x_dims[i] >= y_dims[i]) {
+      (*x_bcast_dims)[i] = 1;
+      (*y_bcast_dims)[i] = x_dims[i] / y_dims[i];
+      bcast_dims_remainder += x_dims[i] % y_dims[i];
+    } else {
+      (*y_bcast_dims)[i] = 1;
+      (*x_bcast_dims)[i] = y_dims[i] / x_dims[i];
+      bcast_dims_remainder += y_dims[i] % x_dims[i];
+    }
+  }
+  PADDLE_ENFORCE_EQ(bcast_dims_remainder,
+                    0,
+                    phi::errors::PreconditionNotMet(
+                        "The input tensor of Op(dist) could not be broadcast, "
+                        "X's shape is [%s], Y's shape is [%s].",
+                        x_dims,
+                        y_dims));
+}
+
+static phi::DDim GetNewDims(const phi::DDim& in_dims, int rank) {
+  std::vector<int64_t> new_dims_vec(rank);
+  if (in_dims.size() < rank) {
+    for (int i = 0; i < rank - in_dims.size(); ++i) {
+      new_dims_vec[i] = 1;
+    }
+    for (int i = 0; i < in_dims.size(); ++i) {
+      new_dims_vec[i + rank - in_dims.size()] = in_dims[i];
+    }
+  } else {
+    new_dims_vec = vectorize(in_dims);
+  }
+  return phi::make_ddim(new_dims_vec);
+}
+
+template <typename Context, typename T, int Rank>
+static void DistFunction(const Context& dev_ctx,
+                         const DenseTensor& x,
+                         const DenseTensor& y,
+                         float p,
+                         DenseTensor* out) {
+  if (out) {
+    dev_ctx.template Alloc<T>(out);
+  }
+  auto x_dims = x.dims();
+  auto y_dims = y.dims();
+
+  // new dims with same size as rank, e.g. (rank=3, (4, 3) => (1, 4, 3))
+  phi::DDim x_new_dims = GetNewDims(x_dims, Rank);
+  phi::DDim y_new_dims = GetNewDims(y_dims, Rank);
+
+  auto x_t = ETensor<T, Rank>::From(x, x_new_dims);
+  auto y_t = ETensor<T, Rank>::From(y, y_new_dims);
+  auto out_t = ETensor<T, 1>::From(*out);
+  auto& place = *dev_ctx.eigen_device();
+
+  Eigen::DSizes<int, Rank> x_bcast_dims;
+  Eigen::DSizes<int, Rank> y_bcast_dims;
+  GetBraodcastDims<Rank>(x_new_dims, y_new_dims, &x_bcast_dims, &y_bcast_dims);
+  // p=0 means number of non-zero elements of (x-y)
+  // p=inf means the maximum of |x-y|
+  // p=-inf means the minimum of |x-y|
+  // otherwise, Lp-norm = pow(sum(pow(|x-y|, p)), 1/p)
+  if (p == 0) {
+    out_t.device(place) =
+        (x_t.broadcast(x_bcast_dims) != y_t.broadcast(y_bcast_dims))
+            .template cast<T>()
+            .sum();
+  } else if (p == INFINITY) {
+    out_t.device(place) =
+        (x_t.broadcast(x_bcast_dims) - y_t.broadcast(y_bcast_dims))
+            .abs()
+            .maximum();
+  } else if (p == -INFINITY) {
+    out_t.device(place) =
+        (x_t.broadcast(x_bcast_dims) - y_t.broadcast(y_bcast_dims))
+            .abs()
+            .minimum();
+  } else {
+    out_t.device(place) =
+        (x_t.broadcast(x_bcast_dims) - y_t.broadcast(y_bcast_dims))
+            .abs()
+            .pow(p)
+            .sum()
+            .pow(1.0 / p);
+  }
+}
+
+template <typename T, typename Context>
+void DistKernel(const Context& dev_ctx,
+                const DenseTensor& x,
+                const DenseTensor& y,
+                float p,
+                DenseTensor* out) {
+  auto x_rank = x.dims().size();
+  auto y_rank = y.dims().size();
+  auto rank = std::max(x_rank, y_rank);
+  PADDLE_ENFORCE_LE(rank,
+                    6,
+                    phi::errors::Unimplemented(
+                        "Op(dist) only support tensors with no more than 6 "
+                        "dimensions, but X's rank is %d, Y's rank is %d.",
+                        x_rank,
+                        y_rank));
+  switch (rank) {
+    case 1:
+      DistFunction<Context, T, 1>(dev_ctx, x, y, p, out);
+      break;
+    case 2:
+      DistFunction<Context, T, 2>(dev_ctx, x, y, p, out);
+      break;
+    case 3:
+      DistFunction<Context, T, 3>(dev_ctx, x, y, p, out);
+      break;
+    case 4:
+      DistFunction<Context, T, 4>(dev_ctx, x, y, p, out);
+      break;
+    case 5:
+      DistFunction<Context, T, 5>(dev_ctx, x, y, p, out);
+      break;
+    case 6:
+      DistFunction<Context, T, 6>(dev_ctx, x, y, p, out);
+      break;
+  }
+}
+
+}  // namespace phi
diff --git a/paddle/phi/ops/compat/dist_sig.cc b/paddle/phi/ops/compat/dist_sig.cc
new file mode 100644
index 0000000000000..18a30b9b84048
--- /dev/null
+++ b/paddle/phi/ops/compat/dist_sig.cc
@@ -0,0 +1,28 @@
+/* Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License. */
+
+#include "paddle/phi/core/compat/op_utils.h"
+
+namespace phi {
+
+KernelSignature DistGradOpArgumentMapping(const ArgumentMappingContext& ctx) {
+  return KernelSignature("dist_grad",
+                         {"X", "Y", "Out", GradVarName("Out")},
+                         {"p"},
+                         {GradVarName("X"), GradVarName("Y")});
+}
+
+}  // namespace phi
+
+PD_REGISTER_ARG_MAPPING_FN(dist_grad, phi::DistGradOpArgumentMapping);