diff --git a/pyciemss/compiled_dynamics.py b/pyciemss/compiled_dynamics.py
index 85248440..cb3b630e 100644
--- a/pyciemss/compiled_dynamics.py
+++ b/pyciemss/compiled_dynamics.py
@@ -29,7 +29,8 @@ def __init__(self, src, **kwargs):
                 "The model parameters could not be compiled. Please check the model definition."
             ) from e
 
-        for k, v in params.items():
+        for k in _sort_dependencies(self.src):
+            v = params[get_name(k)]
             if hasattr(self, get_name(k)):
                 continue
 
@@ -189,6 +190,11 @@ def _compile_deriv(src) -> Callable[..., Tuple[torch.Tensor]]:
     raise NotImplementedError
 
 
+@functools.singledispatch
+def _sort_dependencies(src) -> list:
+    raise NotImplementedError
+
+
 @functools.singledispatch
 def _compile_initial_state(src) -> Callable[..., Tuple[torch.Tensor]]:
     raise NotImplementedError
diff --git a/pyciemss/mira_integration/compiled_dynamics.py b/pyciemss/mira_integration/compiled_dynamics.py
index a427c110..617bf474 100644
--- a/pyciemss/mira_integration/compiled_dynamics.py
+++ b/pyciemss/mira_integration/compiled_dynamics.py
@@ -10,6 +10,7 @@
 import mira.sources.amr
 import numpy
 import pyro
+import pyro.nn
 import sympy
 import sympytorch
 import torch
@@ -20,14 +21,14 @@
     _compile_initial_state,
     _compile_observables,
     _compile_param_values,
+    _sort_dependencies,
     eval_deriv,
     eval_initial_state,
     eval_observables,
     get_name,
 )
 from pyciemss.mira_integration.distributions import (
-    mira_distribution_to_pyro, 
-    sort_mira_dependencies
+    mira_distribution_to_pyro
 )
 
 S = TypeVar("S")
@@ -88,7 +89,7 @@ def _compile_param_values_mira(
     src: mira.modeling.Model,
 ) -> Dict[str, Union[torch.Tensor, pyro.nn.PyroParam, pyro.nn.PyroSample]]:
     values = {}
-    for param_name in sort_mira_dependencies(src):
+    for param_name in _sort_dependencies(src):
         param_info = src.parameters[param_name]
         if param_info.placeholder:
             continue
@@ -102,8 +103,7 @@ def _compile_param_values_mira(
         if isinstance(param_value, torch.nn.Parameter):
             values[param_name] = pyro.nn.PyroParam(param_value)
         elif isinstance(param_value, pyro.distributions.Distribution):
-            # call Distribution.sample() to get the sampled values
-            values[param_name] = param_value.sample()
+            values[param_name] = pyro.sample(param_name, param_value)
         elif isinstance(param_value, (numbers.Number, numpy.ndarray, torch.Tensor)):
             values[param_name] = torch.as_tensor(param_value, dtype=torch.float32)
         else:
diff --git a/pyciemss/mira_integration/distributions.py b/pyciemss/mira_integration/distributions.py
index d29a8570..305f9ec5 100644
--- a/pyciemss/mira_integration/distributions.py
+++ b/pyciemss/mira_integration/distributions.py
@@ -1,25 +1,27 @@
 import warnings
 from typing import Dict, Optional, Union
-from pyciemss.compiled_dynamics import get_name
+
+import mira.modeling
+from pyciemss.compiled_dynamics import get_name, _sort_dependencies
 import mira
 import mira.metamodel
 import networkx as nx
 import pyro
 import torch
 import sympytorch
-from mira.metamodel.utils import safe_parse_expr, SympyExprStr
-
+from mira.metamodel.utils import SympyExprStr
 ParameterDict = Dict[str, Union[torch.Tensor, SympyExprStr]]
 
 
-def sort_mira_dependencies(src: mira.metamodel.TemplateModel) -> list:
+@_sort_dependencies.register(mira.modeling.Model)
+def sort_mira_dependencies(src: mira.modeling.Model) -> list:
     """
     Sort the model parameters of a MIRA TemplateModel by their distribution parameter dependencies.
 
     Parameters
     ----------
-    src : mira.metamodel.TemplateModel
-        The MIRA TemplateModel to sort.
+    src : mira.modeling.Model
+        The MIRA Model to sort.
 
     Returns
     -------
@@ -38,7 +40,8 @@ def sort_mira_dependencies(src: mira.metamodel.TemplateModel) -> list:
                 if isinstance(v, mira.metamodel.utils.SympyExprStr):
                     for free_symbol in v.free_symbols:
                         dependencies.add_edge(str(free_symbol), str(param_name))
-    return  list(nx.topological_sort(dependencies))
+    return list(nx.topological_sort(dependencies))
+
 
 def safe_sympytorch_parse_expr(expr: SympyExprStr, local_dict: Optional[Dict[str, torch.Tensor]]) -> torch.Tensor:
     """