diff --git a/bindings/pydrake/common/BUILD.bazel b/bindings/pydrake/common/BUILD.bazel
index d82666ebf091..06a1bc870093 100644
--- a/bindings/pydrake/common/BUILD.bazel
+++ b/bindings/pydrake/common/BUILD.bazel
@@ -322,6 +322,20 @@ drake_py_library(
     ],
 )
 
+drake_pybind_library(
+    name = "schema_py",
+    cc_deps = [
+        "//bindings/pydrake:documentation_pybind",
+        "//bindings/pydrake:symbolic_types_pybind",
+    ],
+    cc_srcs = ["schema_py.cc"],
+    package_info = PACKAGE_INFO,
+    py_deps = [
+        ":module_py",
+        "//bindings/pydrake:math_py",
+    ],
+)
+
 drake_py_library(
     name = "yaml_py",
     srcs = ["yaml.py"],
@@ -333,6 +347,7 @@ drake_py_library(
 PY_LIBRARIES_WITH_INSTALL = [
     ":_init_py",
     ":eigen_geometry_py",
+    ":schema_py",
     ":value_py",
 ]
 
@@ -598,6 +613,13 @@ drake_py_unittest(
     ],
 )
 
+drake_py_unittest(
+    name = "schema_test",
+    deps = [
+        ":schema_py",
+    ],
+)
+
 drake_py_unittest(
     name = "yaml_test",
     deps = [
diff --git a/bindings/pydrake/common/schema_py.cc b/bindings/pydrake/common/schema_py.cc
new file mode 100644
index 000000000000..a42962ba364f
--- /dev/null
+++ b/bindings/pydrake/common/schema_py.cc
@@ -0,0 +1,229 @@
+#include <memory>
+#include <vector>
+
+#include "pybind11/eigen.h"
+#include "pybind11/pybind11.h"
+#include "pybind11/stl.h"
+
+#include "drake/bindings/pydrake/documentation_pybind.h"
+#include "drake/bindings/pydrake/pydrake_pybind.h"
+#include "drake/bindings/pydrake/symbolic_types_pybind.h"
+#include "drake/common/schema/rotation.h"
+#include "drake/common/schema/stochastic.h"
+#include "drake/common/schema/transform.h"
+
+namespace drake {
+namespace pydrake {
+
+PYBIND11_MODULE(schema, m) {
+  // NOLINTNEXTLINE(build/namespaces): Emulate placement in namespace.
+  using namespace drake::schema;
+  constexpr auto& doc = pydrake_doc.drake.schema;
+
+  m.doc() = "Bindings for the common.schema package.";
+
+  py::module::import("pydrake.common");
+  py::module::import("pydrake.math");
+
+  // Bindings for stochastic.h.
+
+  {
+    using Class = Distribution;
+    constexpr auto& cls_doc = doc.Distribution;
+    py::class_<Class>(m, "Distribution", cls_doc.doc)
+        .def("Sample", &Class::Sample, py::arg("generator"), cls_doc.Sample.doc)
+        .def("Mean", &Class::Mean, cls_doc.Mean.doc)
+        .def("ToSymbolic", &Class::ToSymbolic, cls_doc.ToSymbolic.doc);
+  }
+
+  {
+    using Class = Deterministic;
+    constexpr auto& cls_doc = doc.Deterministic;
+    py::class_<Class, Distribution>(m, "Deterministic", cls_doc.doc)
+        .def(py::init<>(), cls_doc.ctor.doc)
+        .def(py::init<double>(), py::arg("value"), cls_doc.ctor.doc)
+        .def_readwrite("value", &Class::value, cls_doc.value.doc);
+  }
+
+  {
+    using Class = Gaussian;
+    constexpr auto& cls_doc = doc.Gaussian;
+    py::class_<Class, Distribution>(m, "Gaussian", cls_doc.doc)
+        .def(py::init<>(), cls_doc.ctor.doc)
+        .def(py::init<double, double>(), py::arg("mean"), py::arg("stddev"),
+            cls_doc.ctor.doc)
+        .def_readwrite("mean", &Class::mean, cls_doc.mean.doc)
+        .def_readwrite("stddev", &Class::stddev, cls_doc.stddev.doc);
+  }
+
+  {
+    using Class = Uniform;
+    constexpr auto& cls_doc = doc.Uniform;
+    py::class_<Class, Distribution>(m, "Uniform", cls_doc.doc)
+        .def(py::init<>(), cls_doc.ctor.doc)
+        .def(py::init<double, double>(), py::arg("min"), py::arg("max"),
+            cls_doc.ctor.doc)
+        .def_readwrite("min", &Class::min, cls_doc.min.doc)
+        .def_readwrite("max", &Class::max, cls_doc.max.doc);
+  }
+
+  {
+    using Class = UniformDiscrete;
+    constexpr auto& cls_doc = doc.UniformDiscrete;
+    py::class_<Class, Distribution>(m, "UniformDiscrete", cls_doc.doc)
+        .def(py::init<>(), cls_doc.ctor.doc)
+        .def(py::init<std::vector<double>>(), py::arg("values"),
+            cls_doc.ctor.doc)
+        .def_readwrite("values", &Class::values, cls_doc.values.doc);
+  }
+
+  {
+    m  // BR
+        .def("ToDistribution",
+            pydrake::overload_cast_explicit<std::unique_ptr<Distribution>,
+                const DistributionVariant&>(ToDistribution),
+            py::arg("var"), doc.ToDistribution.doc)
+        .def("Sample",
+            pydrake::overload_cast_explicit<double, const DistributionVariant&,
+                drake::RandomGenerator*>(Sample),
+            py::arg("var"), py::arg("generator"),
+            doc.Sample.doc_2args_var_generator)
+        .def("Mean",
+            pydrake::overload_cast_explicit<double, const DistributionVariant&>(
+                Mean),
+            py::arg("var"), doc.Mean.doc_1args_var)
+        .def("ToSymbolic",
+            pydrake::overload_cast_explicit<drake::symbolic::Expression,
+                const DistributionVariant&>(ToSymbolic),
+            py::arg("var"), doc.ToSymbolic.doc_1args_var)
+        .def("IsDeterministic",
+            pydrake::overload_cast_explicit<bool, const DistributionVariant&>(
+                IsDeterministic),
+            py::arg("var"), doc.IsDeterministic.doc_1args_var)
+        .def("GetDeterministicValue",
+            pydrake::overload_cast_explicit<double, const DistributionVariant&>(
+                GetDeterministicValue),
+            py::arg("var"), doc.GetDeterministicValue.doc_1args_var);
+  }
+
+  // TODO(jwnimmer-tri) In the below, we hard-code the template argument `int
+  // Size` to be `Eigen::Dynamic`, i.e., we only bind one of the allowed
+  // values.  In the future, we should also bind Size == 1 through Size == 6
+  // (to match the C++ code).  When we do that, we'll replace the suffix X with
+  // the template pattern `_[Size]`, e.g., `DeterministicVector[3]`.
+
+  {
+    using Class = DistributionVector;
+    constexpr auto& cls_doc = doc.DistributionVector;
+    py::class_<Class>(m, "DistributionVector", cls_doc.doc)
+        .def("Sample", &Class::Sample, py::arg("generator"), cls_doc.Sample.doc)
+        .def("Mean", &Class::Mean, cls_doc.Mean.doc)
+        .def("ToSymbolic", &Class::ToSymbolic, cls_doc.ToSymbolic.doc);
+  }
+
+  {
+    constexpr int size = Eigen::Dynamic;
+    using Class = DeterministicVector<size>;
+    constexpr auto& cls_doc = doc.DeterministicVector;
+    py::class_<Class, DistributionVector>(
+        m, "DeterministicVectorX", cls_doc.doc)
+        .def(py::init<>(), cls_doc.ctor.doc)
+        .def(py::init<const drake::Vector<double, size>&>(), py::arg("value"),
+            cls_doc.ctor.doc)
+        .def_readwrite("value", &Class::value, cls_doc.value.doc);
+  }
+
+  {
+    constexpr int size = Eigen::Dynamic;
+    using Class = GaussianVector<size>;
+    constexpr auto& cls_doc = doc.GaussianVector;
+    py::class_<Class, DistributionVector>(m, "GaussianVectorX", cls_doc.doc)
+        .def(py::init<>(), cls_doc.ctor.doc)
+        .def(py::init<const drake::Vector<double, size>&,
+                 const drake::VectorX<double>&>(),
+            py::arg("mean"), py::arg("stddev"), cls_doc.ctor.doc)
+        .def_readwrite("mean", &Class::mean, cls_doc.mean.doc)
+        .def_readwrite("stddev", &Class::stddev, cls_doc.stddev.doc);
+  }
+
+  {
+    constexpr int size = Eigen::Dynamic;
+    using Class = UniformVector<size>;
+    constexpr auto& cls_doc = doc.UniformVector;
+    py::class_<Class, DistributionVector>(m, "UniformVectorX", cls_doc.doc)
+        .def(py::init<>(), cls_doc.ctor.doc)
+        .def(py::init<const drake::Vector<double, size>&,
+                 const drake::Vector<double, size>&>(),
+            py::arg("min"), py::arg("max"), cls_doc.ctor.doc)
+        .def_readwrite("min", &Class::min, cls_doc.min.doc)
+        .def_readwrite("max", &Class::max, cls_doc.max.doc);
+  }
+
+  {
+    constexpr int size = Eigen::Dynamic;
+    m  // BR
+        .def("ToDistributionVector",
+            pydrake::overload_cast_explicit<std::unique_ptr<DistributionVector>,
+                const DistributionVectorVariant<size>&>(ToDistributionVector),
+            py::arg("vec"), doc.ToDistributionVector.doc)
+        .def("IsDeterministic",
+            pydrake::overload_cast_explicit<bool,
+                const DistributionVectorVariant<size>&>(IsDeterministic),
+            py::arg("vec"),
+            doc.IsDeterministic.doc_1args_constDistributionVectorVariant)
+        .def("GetDeterministicValue",
+            pydrake::overload_cast_explicit<Eigen::VectorXd,
+                const DistributionVectorVariant<size>&>(GetDeterministicValue),
+            py::arg("vec"),
+            doc.GetDeterministicValue.doc_1args_constDistributionVectorVariant);
+  }
+
+  // Bindings for rotation.h.
+
+  {
+    using Class = Rotation;
+    constexpr auto& cls_doc = doc.Rotation;
+    py::class_<Class> cls(m, "Rotation", cls_doc.doc);
+    cls  // BR
+        .def(py::init<>(), cls_doc.ctor.doc_0args)
+        .def(py::init<const math::RotationMatrixd&>(), cls_doc.ctor.doc_1args)
+        .def(py::init<const math::RollPitchYawd&>(), cls_doc.ctor.doc_1args)
+        .def("IsDeterministic", &Class::IsDeterministic,
+            cls_doc.IsDeterministic.doc)
+        .def("GetDeterministicValue", &Class::GetDeterministicValue,
+            cls_doc.GetDeterministicValue.doc)
+        .def("ToSymbolic", &Class::ToSymbolic, cls_doc.ToSymbolic.doc)
+        .def("set_rpy_deg", &Class::set_rpy_deg, py::arg("rpy_deg"),
+            cls_doc.set_rpy_deg.doc);
+    // TODO(jwnimmer-tri) Bind the .value field.
+    // In the meantime, a work-around for read access is to call ToSymbolic or
+    // GetDeterministicValue.
+  }
+
+  // Bindings for transform.h.
+
+  {
+    using Class = Transform;
+    constexpr auto& cls_doc = doc.Transform;
+    py::class_<Class> cls(m, "Transform", cls_doc.doc);
+    cls  // BR
+        .def(py::init<>(), cls_doc.ctor.doc_0args)
+        .def(py::init<const math::RigidTransformd&>(), cls_doc.ctor.doc_1args)
+        .def("set_rotation_rpy_deg", &Class::set_rotation_rpy_deg,
+            py::arg("rpy_deg"), cls_doc.set_rotation_rpy_deg.doc)
+        .def("IsDeterministic", &Class::IsDeterministic,
+            cls_doc.IsDeterministic.doc)
+        .def("GetDeterministicValue", &Class::GetDeterministicValue,
+            cls_doc.GetDeterministicValue.doc)
+        .def("ToSymbolic", &Class::ToSymbolic, cls_doc.ToSymbolic.doc)
+        .def("Sample", &Class::Sample, py::arg("generator"), cls_doc.Sample.doc)
+        .def_readwrite(
+            "base_frame", &Class::base_frame, cls_doc.base_frame.doc);
+    // TODO(jwnimmer-tri) Bind the .translation and .rotation fields.
+    // In the meantime, a work-around for read access is to call ToSymbolic or
+    // GetDeterministicValue.
+  }
+}
+
+}  // namespace pydrake
+}  // namespace drake
diff --git a/bindings/pydrake/common/test/schema_test.py b/bindings/pydrake/common/test/schema_test.py
new file mode 100644
index 000000000000..9861643e6507
--- /dev/null
+++ b/bindings/pydrake/common/test/schema_test.py
@@ -0,0 +1,121 @@
+import unittest
+
+from pydrake.common import RandomGenerator
+import pydrake.common.schema as mut
+import pydrake.math
+
+
+class TestSchema(unittest.TestCase):
+
+    def _check_distribution(self, dut):
+        """Confirms that subclasses of Distribution bind the base methods."""
+        self.assertIsInstance(dut, mut.Distribution)
+        dut.Sample(generator=RandomGenerator())
+        dut.Mean()
+        dut.ToSymbolic()
+
+    def test_deterministic(self):
+        mut.Deterministic()
+        dut = mut.Deterministic(1.0)
+        dut.value = 2.0
+        self._check_distribution(dut)
+
+    def test_gaussian(self):
+        mut.Gaussian()
+        dut = mut.Gaussian(mean=1.0, stddev=0.1)
+        dut.mean = 2.0
+        dut.stddev = 0.2
+        self._check_distribution(dut)
+
+    def test_uniform(self):
+        mut.Uniform()
+        dut = mut.Uniform(min=-1.0, max=1.0)
+        dut.min = -2.0
+        dut.max = 2.0
+        self._check_distribution(dut)
+
+    def test_uniform_discrete(self):
+        mut.UniformDiscrete()
+        dut = mut.UniformDiscrete(values=[0.0, 0.1])
+        dut.values = [0.0, 0.2]
+        self._check_distribution(dut)
+
+    def test_distribution_variant(self):
+        """Confirms that the free functions that operate on a variant are
+        bound."""
+        items = [
+            mut.Deterministic(1.0),
+            mut.Gaussian(1.0, 0.1),
+            mut.Uniform(-1.0, 1.0),
+            mut.UniformDiscrete([0.0, 1.0]),
+        ]
+        for item in items:
+            copied = mut.ToDistribution(item)
+            self._check_distribution(copied)
+            mut.Sample(var=item, generator=RandomGenerator())
+            mut.Mean(var=item)
+            mut.ToSymbolic(var=item)
+            if mut.IsDeterministic(var=item):
+                mut.GetDeterministicValue(var=item)
+
+    def _check_distribution_vector(self, dut):
+        """Confirms that subclasses of DistributionVector bind the base
+        methods.
+        """
+        self.assertIsInstance(dut, mut.DistributionVector)
+        dut.Sample(generator=RandomGenerator())
+        dut.Mean()
+        dut.ToSymbolic()
+
+    def test_deterministic_vector(self):
+        mut.DeterministicVectorX()
+        dut = mut.DeterministicVectorX(value=[0.0, 1.0])
+        dut.value = [0.0, 2.0]
+        self._check_distribution_vector(dut)
+
+    def test_gaussian_vector(self):
+        mut.GaussianVectorX()
+        dut = mut.GaussianVectorX(mean=[-1.0, 1.0], stddev=[0.1, 0.1])
+        dut.mean = [-2.0, 2.0]
+        dut.stddev = [0.2, 0.2]
+        self._check_distribution_vector(dut)
+
+    def test_uniform_vector(self):
+        mut.UniformVectorX()
+        dut = mut.UniformVectorX(min=[-1.0, -10.0], max=[1.0, 10.0])
+        dut.min = [-2.0, -20.0]
+        dut.max = [2.0, 20.0]
+        self._check_distribution_vector(dut)
+
+    def test_distribution_vector_variant(self):
+        """Confirms that the free functions that operate on a vector variant
+        are bound."""
+        items = [
+            mut.DeterministicVectorX(value=[1.0]),
+            mut.GaussianVectorX(mean=[1.0], stddev=[0.1]),
+            mut.UniformVectorX(min=[-1.0], max=[1.0]),
+        ]
+        for item in items:
+            copied = mut.ToDistributionVector(item)
+            self._check_distribution_vector(copied)
+            if mut.IsDeterministic(vec=item):
+                mut.GetDeterministicValue(vec=item)
+
+    def test_rotation(self):
+        mut.Rotation()
+        mut.Rotation(pydrake.math.RotationMatrix())
+        dut = mut.Rotation(pydrake.math.RollPitchYaw([0.0, 0.0, 0.0]))
+        dut.IsDeterministic()
+        dut.GetDeterministicValue()
+        dut.ToSymbolic()
+        dut.set_rpy_deg([0.1, 0.2, 0.3])
+
+    def test_transform(self):
+        mut.Transform()
+        dut = mut.Transform(pydrake.math.RigidTransform())
+        dut.set_rotation_rpy_deg([0.1, 0.2, 0.3])
+        dut.IsDeterministic()
+        dut.GetDeterministicValue()
+        dut.ToSymbolic()
+        dut.Sample(generator=RandomGenerator())
+        dut.base_frame = "name"
diff --git a/common/schema/transform.cc b/common/schema/transform.cc
index 7306139b13df..80415940eff4 100644
--- a/common/schema/transform.cc
+++ b/common/schema/transform.cc
@@ -60,7 +60,7 @@ math::RigidTransformd Transform::Mean() const {
 }
 
 math::RigidTransformd Transform::Sample(
-    RandomGenerator* random) const {
+    RandomGenerator* generator) const {
   // It is somewhat yak-shavey to get an actual materialized transform here.
   // We convert to symbolic, convert the symbolic to a vector and matrix of
   // symbolic, `Evaluate` those, convert the result back to a
@@ -76,12 +76,12 @@ math::RigidTransformd Transform::Sample(
   const Vector3<Expression> symbolic_translation =
       symbolic_transform.translation();
   const Eigen::Vector3d concrete_translation =
-      symbolic::Evaluate(symbolic_translation, {}, random);
+      symbolic::Evaluate(symbolic_translation, {}, generator);
 
   const math::RotationMatrix<Expression> symbolic_rotation =
       symbolic_transform.rotation();
   const math::RotationMatrixd concrete_rotation(
-      symbolic::Evaluate(symbolic_rotation.matrix(), {}, random));
+      symbolic::Evaluate(symbolic_rotation.matrix(), {}, generator));
 
   return math::RigidTransformd{concrete_rotation, concrete_translation};
 }
diff --git a/common/schema/transform.h b/common/schema/transform.h
index 1366af14481a..256f14f653a4 100644
--- a/common/schema/transform.h
+++ b/common/schema/transform.h
@@ -186,7 +186,7 @@ class Transform {
 
   /// Samples this Transform.  If this is deterministic, the result is the same
   /// as GetDeterministicValue.
-  math::RigidTransformd Sample(RandomGenerator* random) const;
+  math::RigidTransformd Sample(RandomGenerator* generator) const;
 
   template <typename Archive>
   void Serialize(Archive* a) {