diff --git a/pymc3/distributions/continuous.py b/pymc3/distributions/continuous.py
index 81793143bf..cf68949121 100644
--- a/pymc3/distributions/continuous.py
+++ b/pymc3/distributions/continuous.py
@@ -308,31 +308,36 @@ def logcdf(value, lower, upper):
         )
 
 
+class FlatRV(RandomVariable):
+    name = "flat"
+    ndim_supp = 0
+    ndims_params = []
+    dtype = "floatX"
+    _print_name = ("Flat", "\\operatorname{Flat}")
+
+    @classmethod
+    def rng_fn(cls, rng, size):
+        raise NotImplementedError("Cannot sample from flat variable")
+
+
+flat = FlatRV()
+
+
 class Flat(Continuous):
     """
     Uninformative log-likelihood that returns 0 regardless of
     the passed value.
     """
 
-    def __init__(self, *args, **kwargs):
-        self._default = 0
-        super().__init__(defaults=("_default",), *args, **kwargs)
-
-    def random(self, point=None, size=None):
-        """Raises ValueError as it is not possible to sample from Flat distribution
-
-        Parameters
-        ----------
-        point: dict, optional
-        size: int, optional
+    rv_op = flat
 
-        Raises
-        -------
-        ValueError
-        """
-        raise ValueError("Cannot sample from Flat distribution")
+    @classmethod
+    def dist(cls, *, size=None, testval=None, **kwargs):
+        if testval is None:
+            testval = np.full(size, floatX(0.0))
+        return super().dist([], size=size, testval=testval, **kwargs)
 
-    def logp(self, value):
+    def logp(value):
         """
         Calculate log-probability of Flat distribution at specified value.
 
@@ -348,7 +353,7 @@ def logp(self, value):
         """
         return at.zeros_like(value)
 
-    def logcdf(self, value):
+    def logcdf(value):
         """
         Compute the log of the cumulative distribution function for Flat distribution
         at the specified value.
@@ -368,28 +373,33 @@ def logcdf(self, value):
         )
 
 
-class HalfFlat(PositiveContinuous):
-    """Improper flat prior over the positive reals."""
+class HalfFlatRV(RandomVariable):
+    name = "half_flat"
+    ndim_supp = 0
+    ndims_params = []
+    dtype = "floatX"
+    _print_name = ("HalfFlat", "\\operatorname{HalfFlat}")
 
-    def __init__(self, *args, **kwargs):
-        self._default = 1
-        super().__init__(defaults=("_default",), *args, **kwargs)
+    @classmethod
+    def rng_fn(cls, rng, size):
+        raise NotImplementedError("Cannot sample from half_flat variable")
 
-    def random(self, point=None, size=None):
-        """Raises ValueError as it is not possible to sample from HalfFlat distribution
 
-        Parameters
-        ----------
-        point: dict, optional
-        size: int, optional
+halfflat = HalfFlatRV()
 
-        Raises
-        -------
-        ValueError
-        """
-        raise ValueError("Cannot sample from HalfFlat distribution")
 
-    def logp(self, value):
+class HalfFlat(PositiveContinuous):
+    """Improper flat prior over the positive reals."""
+
+    rv_op = halfflat
+
+    @classmethod
+    def dist(cls, *, size=None, testval=None, **kwargs):
+        if testval is None:
+            testval = np.full(size, floatX(1.0))
+        return super().dist([], size=size, testval=testval, **kwargs)
+
+    def logp(value):
         """
         Calculate log-probability of HalfFlat distribution at specified value.
 
@@ -405,7 +415,7 @@ def logp(self, value):
         """
         return bound(at.zeros_like(value), value > 0)
 
-    def logcdf(self, value):
+    def logcdf(value):
         """
         Compute the log of the cumulative distribution function for HalfFlat distribution
         at the specified value.
diff --git a/pymc3/tests/test_distributions.py b/pymc3/tests/test_distributions.py
index 9b7a3bbee6..c59f8f567b 100644
--- a/pymc3/tests/test_distributions.py
+++ b/pymc3/tests/test_distributions.py
@@ -961,7 +961,6 @@ def test_discrete_unif(self):
             assert logpt(invalid_dist, 0.5).eval() == -np.inf
             assert logcdf(invalid_dist, 2).eval() == -np.inf
 
-    @pytest.mark.xfail(reason="Distribution not refactored yet")
     def test_flat(self):
         self.check_logp(Flat, Runif, {}, lambda value: 0)
         with Model():
@@ -969,10 +968,9 @@ def test_flat(self):
             assert_allclose(x.tag.test_value, 0)
         self.check_logcdf(Flat, R, {}, lambda value: np.log(0.5))
         # Check infinite cases individually.
-        assert 0.0 == logcdf(Flat.dist(), np.inf).tag.test_value
-        assert -np.inf == logcdf(Flat.dist(), -np.inf).tag.test_value
+        assert 0.0 == logcdf(Flat.dist(), np.inf).eval()
+        assert -np.inf == logcdf(Flat.dist(), -np.inf).eval()
 
-    @pytest.mark.xfail(reason="Distribution not refactored yet")
     def test_half_flat(self):
         self.check_logp(HalfFlat, Rplus, {}, lambda value: 0)
         with Model():
@@ -981,8 +979,8 @@ def test_half_flat(self):
             assert x.tag.test_value.shape == (2,)
         self.check_logcdf(HalfFlat, Rplus, {}, lambda value: -np.inf)
         # Check infinite cases individually.
-        assert 0.0 == logcdf(HalfFlat.dist(), np.inf).tag.test_value
-        assert -np.inf == logcdf(HalfFlat.dist(), -np.inf).tag.test_value
+        assert 0.0 == logcdf(HalfFlat.dist(), np.inf).eval()
+        assert -np.inf == logcdf(HalfFlat.dist(), -np.inf).eval()
 
     def test_normal(self):
         self.check_logp(
@@ -2499,17 +2497,19 @@ def test_vonmises(self):
             lambda value, mu, kappa: floatX(sp.vonmises.logpdf(value, kappa, loc=mu)),
         )
 
-    @pytest.mark.xfail(reason="Distribution not refactored yet")
     def test_gumbel(self):
-        def gumbel(value, mu, beta):
-            return floatX(sp.gumbel_r.logpdf(value, loc=mu, scale=beta))
-
-        self.check_logp(Gumbel, R, {"mu": R, "beta": Rplusbig}, gumbel)
-
-        def gumbellcdf(value, mu, beta):
-            return floatX(sp.gumbel_r.logcdf(value, loc=mu, scale=beta))
-
-        self.check_logcdf(Gumbel, R, {"mu": R, "beta": Rplusbig}, gumbellcdf)
+        self.check_logp(
+            Gumbel,
+            R,
+            {"mu": R, "beta": Rplusbig},
+            lambda value, mu, beta: sp.gumbel_r.logpdf(value, loc=mu, scale=beta),
+        )
+        self.check_logcdf(
+            Gumbel,
+            R,
+            {"mu": R, "beta": Rplusbig},
+            lambda value, mu, beta: sp.gumbel_r.logcdf(value, loc=mu, scale=beta),
+        )
 
     def test_logistic(self):
         self.check_logp(
@@ -2538,11 +2538,6 @@ def test_logitnormal(self):
             decimal=select_by_precision(float64=6, float32=1),
         )
 
-    @pytest.mark.xfail(reason="Distribution not refactored yet")
-    def test_multidimensional_beta_construction(self):
-        with Model():
-            Beta("beta", alpha=1.0, beta=1.0, size=(10, 20))
-
     @pytest.mark.xfail(
         condition=(aesara.config.floatX == "float32"),
         reason="Some combinations underflow to -inf in float32 in pymc version",
diff --git a/pymc3/tests/test_distributions_random.py b/pymc3/tests/test_distributions_random.py
index 3d35a9a98d..88e56aa480 100644
--- a/pymc3/tests/test_distributions_random.py
+++ b/pymc3/tests/test_distributions_random.py
@@ -360,7 +360,11 @@ def check_rv_size(self):
             assert actual == expected, f"size={size}, expected={expected}, actual={actual}"
 
         # test multi-parameters sampling for univariate distributions (with univariate inputs)
-        if self.pymc_dist.rv_op.ndim_supp == 0 and sum(self.pymc_dist.rv_op.ndims_params) == 0:
+        if (
+            self.pymc_dist.rv_op.ndim_supp == 0
+            and self.pymc_dist.rv_op.ndims_params
+            and sum(self.pymc_dist.rv_op.ndims_params) == 0
+        ):
             params = {
                 k: p * np.ones(self.repeated_params_shape) for k, p in self.pymc_dist_params.items()
             }
@@ -394,6 +398,36 @@ def seeded_numpy_distribution_builder(dist_name: str) -> Callable:
     )
 
 
+class TestFlat(BaseTestDistribution):
+    pymc_dist = pm.Flat
+    pymc_dist_params = {}
+    expected_rv_op_params = {}
+    tests_to_run = [
+        "check_pymc_params_match_rv_op",
+        "check_rv_size",
+        "check_not_implemented",
+    ]
+
+    def check_not_implemented(self):
+        with pytest.raises(NotImplementedError):
+            self.pymc_rv.eval()
+
+
+class TestHalfFlat(BaseTestDistribution):
+    pymc_dist = pm.HalfFlat
+    pymc_dist_params = {}
+    expected_rv_op_params = {}
+    tests_to_run = [
+        "check_pymc_params_match_rv_op",
+        "check_rv_size",
+        "check_not_implemented",
+    ]
+
+    def check_not_implemented(self):
+        with pytest.raises(NotImplementedError):
+            self.pymc_rv.eval()
+
+
 class TestDiscreteWeibull(BaseTestDistribution):
     def discrete_weibul_rng_fn(self, size, q, beta, uniform_rng_fct):
         return np.ceil(np.power(np.log(1 - uniform_rng_fct(size=size)) / np.log(q), 1.0 / beta)) - 1
@@ -1240,20 +1274,6 @@ def ref_rand(size, mu, sigma, nu):
 
         pymc3_random(pm.ExGaussian, {"mu": R, "sigma": Rplus, "nu": Rplus}, ref_rand=ref_rand)
 
-    @pytest.mark.xfail(reason="This distribution has not been refactored for v4")
-    def test_flat(self):
-        with pm.Model():
-            f = pm.Flat("f")
-            with pytest.raises(ValueError):
-                f.random(1)
-
-    @pytest.mark.xfail(reason="This distribution has not been refactored for v4")
-    def test_half_flat(self):
-        with pm.Model():
-            f = pm.HalfFlat("f")
-            with pytest.raises(ValueError):
-                f.random(1)
-
     @pytest.mark.xfail(reason="This distribution has not been refactored for v4")
     def test_matrix_normal(self):
         def ref_rand(size, mu, rowcov, colcov):
diff --git a/pymc3/tests/test_distributions_timeseries.py b/pymc3/tests/test_distributions_timeseries.py
index 5f9ec3485d..4f55d90214 100644
--- a/pymc3/tests/test_distributions_timeseries.py
+++ b/pymc3/tests/test_distributions_timeseries.py
@@ -23,7 +23,7 @@
 from pymc3.tests.helpers import select_by_precision
 
 # pytestmark = pytest.mark.usefixtures("seeded_test")
-pytestmark = pytest.mark.xfail(reason="This test relies on the deprecated Distribution interface")
+pytestmark = pytest.mark.xfail(reason="Timeseries not refactored")
 
 
 def test_AR():
diff --git a/pymc3/tests/test_sampling.py b/pymc3/tests/test_sampling.py
index 009346b9e4..46a2a86915 100644
--- a/pymc3/tests/test_sampling.py
+++ b/pymc3/tests/test_sampling.py
@@ -603,7 +603,6 @@ def test_sum_normal(self):
             _, pval = stats.kstest(ppc["b"], stats.norm(scale=scale).cdf)
             assert pval > 0.001
 
-    @pytest.mark.xfail(reason="HalfFlat not refactored for v4")
     def test_model_not_drawable_prior(self):
         data = np.random.poisson(lam=10, size=200)
         model = pm.Model()
@@ -613,7 +612,7 @@ def test_model_not_drawable_prior(self):
             trace = pm.sample(tune=1000)
 
         with model:
-            with pytest.raises(ValueError) as excinfo:
+            with pytest.raises(NotImplementedError) as excinfo:
                 pm.sample_prior_predictive(50)
             assert "Cannot sample" in str(excinfo.value)
             samples = pm.sample_posterior_predictive(trace, 40)
diff --git a/pymc3/tests/test_step.py b/pymc3/tests/test_step.py
index fd02139879..27fffe6ad4 100644
--- a/pymc3/tests/test_step.py
+++ b/pymc3/tests/test_step.py
@@ -621,7 +621,7 @@ def test_step_categorical(self):
             trace = sample(8000, tune=0, step=step, start=start, model=model, random_seed=1)
             self.check_stat(check, trace, step.__class__.__name__)
 
-    @pytest.mark.xfail(reason="Flat not refactored for v4")
+    @pytest.mark.xfail(reason="EllipticalSlice not refactored for v4")
     def test_step_elliptical_slice(self):
         start, model, (K, L, mu, std, noise) = mv_prior_simple()
         unc = noise ** 0.5