diff --git a/CHANGELOG.md b/CHANGELOG.md
index 877a367b28b2..1be0426da651 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,6 +5,7 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 
 ## [2.0.5] - 2022-MM-DD
 ### Added
+- Added `AddPositionalEncoding` transform ([#4521](https://github.com/pyg-team/pytorch_geometric/pull/4521))
 - Added `HeteroData.is_undirected()` support ([#4604](https://github.com/pyg-team/pytorch_geometric/pull/4604))
 - Added the `Genius` and `Wiki` datasets to `nn.datasets.LINKXDataset` ([#4570](https://github.com/pyg-team/pytorch_geometric/pull/4570), [#4600](https://github.com/pyg-team/pytorch_geometric/pull/4600))
 - Added `nn.glob.GlobalPooling` module with support for multiple aggregations ([#4582](https://github.com/pyg-team/pytorch_geometric/pull/4582))
diff --git a/test/transforms/test_add_positional_encoding.py b/test/transforms/test_add_positional_encoding.py
new file mode 100644
index 000000000000..ab64a3490c54
--- /dev/null
+++ b/test/transforms/test_add_positional_encoding.py
@@ -0,0 +1,93 @@
+import copy
+
+import torch
+
+from torch_geometric.data import Data
+from torch_geometric.transforms import (
+    AddLaplacianEigenvectorPE,
+    AddRandomWalkPE,
+)
+
+
+def test_add_laplacian_eigenvector_pe():
+    x = torch.randn(6, 4)
+    edge_index = torch.tensor([[0, 1, 0, 4, 1, 4, 2, 3, 3, 5],
+                               [1, 0, 4, 0, 4, 1, 3, 2, 5, 3]])
+    data = Data(x=x, edge_index=edge_index)
+
+    transform = AddLaplacianEigenvectorPE(k=3)
+    assert str(transform) == 'AddLaplacianEigenvectorPE()'
+    out = transform(copy.copy(data))
+    assert out.laplacian_eigenvector_pe.size() == (6, 3)
+
+    transform = AddLaplacianEigenvectorPE(k=3, attr_name=None)
+    out = transform(copy.copy(data))
+    assert out.x.size() == (6, 4 + 3)
+
+    transform = AddLaplacianEigenvectorPE(k=3, attr_name='x')
+    out = transform(copy.copy(data))
+    assert out.x.size() == (6, 3)
+
+    # Output tests:
+    edge_index = torch.tensor([[0, 1, 0, 4, 1, 4, 2, 3, 3, 5, 2, 5],
+                               [1, 0, 4, 0, 4, 1, 3, 2, 5, 3, 5, 2]])
+    data = Data(x=x, edge_index=edge_index)
+
+    transform1 = AddLaplacianEigenvectorPE(k=1, is_undirected=True)
+    transform2 = AddLaplacianEigenvectorPE(k=1, is_undirected=False)
+
+    # Clustering test with first non-trivial eigenvector (Fiedler vector)
+    pe = transform1(copy.copy(data)).laplacian_eigenvector_pe
+    pe_cluster_1 = pe[[0, 1, 4]]
+    pe_cluster_2 = pe[[2, 3, 5]]
+    assert not torch.allclose(pe_cluster_1, pe_cluster_2)
+    assert torch.allclose(pe_cluster_1, pe_cluster_1.mean())
+    assert torch.allclose(pe_cluster_2, pe_cluster_2.mean())
+
+    pe = transform2(copy.copy(data)).laplacian_eigenvector_pe
+    pe_cluster_1 = pe[[0, 1, 4]]
+    pe_cluster_2 = pe[[2, 3, 5]]
+    assert not torch.allclose(pe_cluster_1, pe_cluster_2)
+    assert torch.allclose(pe_cluster_1, pe_cluster_1.mean())
+    assert torch.allclose(pe_cluster_2, pe_cluster_2.mean())
+
+
+def test_add_random_walk_pe():
+    x = torch.randn(6, 4)
+    edge_index = torch.tensor([[0, 1, 0, 4, 1, 4, 2, 3, 3, 5],
+                               [1, 0, 4, 0, 4, 1, 3, 2, 5, 3]])
+    data = Data(x=x, edge_index=edge_index)
+
+    transform = AddRandomWalkPE(walk_length=3)
+    assert str(transform) == 'AddRandomWalkPE()'
+    out = transform(copy.copy(data))
+    assert out.random_walk_pe.size() == (6, 3)
+
+    transform = AddRandomWalkPE(walk_length=3, attr_name=None)
+    out = transform(copy.copy(data))
+    assert out.x.size() == (6, 4 + 3)
+
+    transform = AddRandomWalkPE(walk_length=3, attr_name='x')
+    out = transform(copy.copy(data))
+    assert out.x.size() == (6, 3)
+
+    # Output tests:
+    assert out.x.tolist() == [
+        [0.0, 0.5, 0.25],
+        [0.0, 0.5, 0.25],
+        [0.0, 0.5, 0.00],
+        [0.0, 1.0, 0.00],
+        [0.0, 0.5, 0.25],
+        [0.0, 0.5, 0.00],
+    ]
+
+    edge_index = torch.tensor([[0, 1, 2], [0, 1, 2]])
+    data = Data(edge_index=edge_index, num_nodes=4)
+    out = transform(copy.copy(data))
+
+    assert out.x.tolist() == [
+        [1.0, 1.0, 1.0],
+        [1.0, 1.0, 1.0],
+        [1.0, 1.0, 1.0],
+        [0.0, 0.0, 0.0],
+    ]
diff --git a/test/utils/test_loop.py b/test/utils/test_loop.py
index cf245befcd51..ded7a69cb091 100644
--- a/test/utils/test_loop.py
+++ b/test/utils/test_loop.py
@@ -4,6 +4,7 @@
     add_remaining_self_loops,
     add_self_loops,
     contains_self_loops,
+    get_self_loop_attr,
     remove_self_loops,
     segregate_self_loops,
 )
@@ -103,3 +104,21 @@ def test_add_remaining_self_loops_without_initial_loops():
     edge_index, edge_weight = add_remaining_self_loops(edge_index, edge_weight)
     assert edge_index.tolist() == [[0, 1, 0, 1], [1, 0, 0, 1]]
     assert edge_weight.tolist() == [0.5, 0.5, 1, 1]
+
+
+def test_get_self_loop_attr():
+    edge_index = torch.tensor([[0, 1, 0], [1, 0, 0]])
+    edge_weight = torch.tensor([0.2, 0.3, 0.5])
+
+    full_loop_weight = get_self_loop_attr(edge_index, edge_weight)
+    assert full_loop_weight.tolist() == [0.5, 0.0]
+
+    full_loop_weight = get_self_loop_attr(edge_index, edge_weight, num_nodes=4)
+    assert full_loop_weight.tolist() == [0.5, 0.0, 0.0, 0.0]
+
+    full_loop_weight = get_self_loop_attr(edge_index)
+    assert full_loop_weight.tolist() == [1.0, 0.0]
+
+    edge_attr = torch.tensor([[1.0, 0.0], [0.0, 1.0], [0.5, 1.0]])
+    full_loop_attr = get_self_loop_attr(edge_index, edge_attr)
+    assert full_loop_attr.tolist() == [[0.5, 1.0], [0.0, 0.0]]
diff --git a/torch_geometric/transforms/__init__.py b/torch_geometric/transforms/__init__.py
index deb6fe11c28b..fbd52180fdb8 100644
--- a/torch_geometric/transforms/__init__.py
+++ b/torch_geometric/transforms/__init__.py
@@ -48,6 +48,7 @@
 from .add_metapaths import AddMetaPaths
 from .largest_connected_components import LargestConnectedComponents
 from .virtual_node import VirtualNode
+from .add_positional_encoding import AddLaplacianEigenvectorPE, AddRandomWalkPE
 
 __all__ = [
     'BaseTransform',
@@ -100,6 +101,8 @@
     'AddMetaPaths',
     'LargestConnectedComponents',
     'VirtualNode',
+    'AddLaplacianEigenvectorPE',
+    'AddRandomWalkPE',
 ]
 
 classes = __all__
diff --git a/torch_geometric/transforms/add_positional_encoding.py b/torch_geometric/transforms/add_positional_encoding.py
new file mode 100644
index 000000000000..05aed9387dc0
--- /dev/null
+++ b/torch_geometric/transforms/add_positional_encoding.py
@@ -0,0 +1,139 @@
+from typing import Any, Optional
+
+import numpy as np
+import torch
+from torch_sparse import SparseTensor
+
+from torch_geometric.data import Data
+from torch_geometric.data.datapipes import functional_transform
+from torch_geometric.transforms import BaseTransform
+from torch_geometric.utils import (
+    get_laplacian,
+    get_self_loop_attr,
+    to_scipy_sparse_matrix,
+)
+
+
+def add_node_attr(data: Data, value: Any,
+                  attr_name: Optional[str] = None) -> Data:
+    # TODO Move to `BaseTransform`.
+    if attr_name is None:
+        if 'x' in data:
+            x = data.x.view(-1, 1) if data.x.dim() == 1 else data.x
+            data.x = torch.cat([x, value.to(x.device, x.dtype)], dim=-1)
+        else:
+            data.x = value
+    else:
+        data[attr_name] = value
+
+    return data
+
+
+@functional_transform('add_laplacian_eigenvector_pe')
+class AddLaplacianEigenvectorPE(BaseTransform):
+    r"""Adds the Laplacian eigenvector positional encoding from the
+    `"Benchmarking Graph Neural Networks" <https://arxiv.org/abs/2003.00982>`_
+    paper to the given graph
+    (functional name: :obj:`add_laplacian_eigenvector_pe`).
+
+    Args:
+        k (int): The number of non-trivial eigenvectors to consider.
+        attr_name (str, optional): The attribute name of the data object to add
+            positional encodings to. If set to :obj:`None`, will be
+            concatenated to :obj:`data.x`.
+            (default: :obj:`"laplacian_eigenvector_pe"`)
+        is_undirected (bool, optional): If set to :obj:`True`, this transform
+            expects undirected graphs as input, and can hence speed up the
+            computation of eigenvectors. (default: :obj:`False`)
+        **kwargs (optional): Additional arguments of
+            :meth:`scipy.sparse.linalg.eigs` (when :attr:`is_undirected` is
+            :obj:`False`) or :meth:`scipy.sparse.linalg.eigsh` (when
+            :attr:`is_undirected` is :obj:`True`).
+    """
+    def __init__(
+        self,
+        k: int,
+        attr_name: Optional[str] = 'laplacian_eigenvector_pe',
+        is_undirected: bool = False,
+        **kwargs,
+    ):
+        self.k = k
+        self.attr_name = attr_name
+        self.is_undirected = is_undirected
+        self.kwargs = kwargs
+
+    def __call__(self, data: Data) -> Data:
+        from scipy.sparse.linalg import eigs, eigsh
+        eig_fn = eigs if not self.is_undirected else eigsh
+
+        num_nodes = data.num_nodes
+        edge_index, edge_weight = get_laplacian(
+            data.edge_index,
+            normalization='sym',
+            num_nodes=num_nodes,
+        )
+
+        L = to_scipy_sparse_matrix(edge_index, edge_weight, num_nodes)
+
+        eig_vals, eig_vecs = eig_fn(
+            L,
+            k=self.k + 1,
+            which='SR' if not self.is_undirected else 'SA',
+            return_eigenvectors=True,
+            **self.kwargs,
+        )
+
+        eig_vecs = np.real(eig_vecs[:, eig_vals.argsort()])
+        pe = torch.from_numpy(eig_vecs[:, 1:self.k + 1])
+        sign = -1 + 2 * torch.randint(0, 2, (self.k, ))
+        pe *= sign
+
+        data = add_node_attr(data, pe, attr_name=self.attr_name)
+        return data
+
+
+@functional_transform('add_random_walk_pe')
+class AddRandomWalkPE(BaseTransform):
+    r"""Adds the random walk positional encoding from the `"Graph Neural
+    Networks with Learnable Structural and Positional Representations"
+    <https://arxiv.org/abs/2110.07875>`_ paper to the given graph
+    (functional name: :obj:`add_random_walk_pe`).
+
+    Args:
+        walk_length (int): The number of random walk steps.
+        attr_name (str, optional): The attribute name of the data object to add
+            positional encodings to. If set to :obj:`None`, will be
+            concatenated to :obj:`data.x`.
+            (default: :obj:`"laplacian_eigenvector_pe"`)
+    """
+    def __init__(
+        self,
+        walk_length: int,
+        attr_name: Optional[str] = 'random_walk_pe',
+    ):
+        self.walk_length = walk_length
+        self.attr_name = attr_name
+
+    def __call__(self, data: Data) -> Data:
+        num_nodes = data.num_nodes
+        edge_index, edge_weight = data.edge_index, data.edge_weight
+
+        adj = SparseTensor.from_edge_index(edge_index, edge_weight,
+                                           sparse_sizes=(num_nodes, num_nodes))
+
+        # Compute D^{-1} A:
+        deg_inv = 1.0 / adj.sum(dim=1)
+        deg_inv[deg_inv == float('inf')] = 0
+        adj = adj * deg_inv.view(-1, 1)
+
+        out = adj
+        row, col, value = out.coo()
+        pe_list = [get_self_loop_attr((row, col), value, num_nodes)]
+        for _ in range(self.walk_length - 1):
+            out = out @ adj
+            row, col, value = out.coo()
+            pe_list.append(get_self_loop_attr((row, col), value, num_nodes))
+        pe = torch.stack(pe_list, dim=-1)
+
+        data = add_node_attr(data, pe, attr_name=self.attr_name)
+        return data
diff --git a/torch_geometric/utils/__init__.py b/torch_geometric/utils/__init__.py
index 64c77fbda34e..a9c09230d6c0 100644
--- a/torch_geometric/utils/__init__.py
+++ b/torch_geometric/utils/__init__.py
@@ -6,7 +6,7 @@
 from .undirected import is_undirected, to_undirected
 from .loop import (contains_self_loops, remove_self_loops,
                    segregate_self_loops, add_self_loops,
-                   add_remaining_self_loops)
+                   add_remaining_self_loops, get_self_loop_attr)
 from .isolated import contains_isolated_nodes, remove_isolated_nodes
 from .subgraph import (get_num_hops, subgraph, k_hop_subgraph,
                        bipartite_subgraph)
@@ -46,6 +46,7 @@
     'segregate_self_loops',
     'add_self_loops',
     'add_remaining_self_loops',
+    'get_self_loop_attr',
     'contains_isolated_nodes',
     'remove_isolated_nodes',
     'get_num_hops',
diff --git a/torch_geometric/utils/loop.py b/torch_geometric/utils/loop.py
index 2d50d6004867..7c08b322d112 100644
--- a/torch_geometric/utils/loop.py
+++ b/torch_geometric/utils/loop.py
@@ -227,3 +227,39 @@ def add_remaining_self_loops(
 
     edge_index = torch.cat([edge_index[:, mask], loop_index], dim=1)
     return edge_index, edge_attr
+
+
+def get_self_loop_attr(edge_index: Tensor, edge_attr: OptTensor = None,
+                       num_nodes: Optional[int] = None) -> Tensor:
+    r"""Returns the edge features or weights of self-loops
+    :math:`(i, i)` of every node :math:`i \in \mathcal{V}` in the
+    graph given by :attr:`edge_index`. Edge features of missing self-loops not
+    present in :attr:`edge_index` will be filled with zeros. If
+    :attr:`edge_attr` is not given, it will be the vector of ones.
+
+    .. note::
+        This operation is analogous to getting the diagonal elements of the
+        dense adjacency matrix.
+
+    Args:
+        edge_index (LongTensor): The edge indices.
+        edge_attr (Tensor, optional): Edge weights or multi-dimensional edge
+            features. (default: :obj:`None`)
+        num_nodes (int, optional): The number of nodes, *i.e.*
+            :obj:`max_val + 1` of :attr:`edge_index`. (default: :obj:`None`)
+
+    :rtype: :class:`Tensor`
+    """
+    loop_mask = edge_index[0] == edge_index[1]
+    loop_index = edge_index[0][loop_mask]
+
+    if edge_attr is not None:
+        loop_attr = edge_attr[loop_mask]
+    else:  # A vector of ones:
+        loop_attr = torch.ones_like(loop_index, dtype=torch.float)
+
+    num_nodes = maybe_num_nodes(edge_index, num_nodes)
+    full_loop_attr = loop_attr.new_zeros((num_nodes, ) + loop_attr.size()[1:])
+    full_loop_attr[loop_index] = loop_attr
+
+    return full_loop_attr