diff --git a/src/moscot/base/problems/compound_problem.py b/src/moscot/base/problems/compound_problem.py
index 0f6f7462..eef27314 100644
--- a/src/moscot/base/problems/compound_problem.py
+++ b/src/moscot/base/problems/compound_problem.py
@@ -313,6 +313,11 @@ def solve(
         problems = self._problem_manager.get_problems(stage=stage)
 
         logger.info(f"Solving `{len(problems)}` problems")
+        # expose min/max iterations to the user but remove them if they are None
+        if "min_iterations" in kwargs and kwargs["min_iterations"] is None:
+            kwargs.pop("min_iterations")
+        if "max_iterations" in kwargs and kwargs["max_iterations"] is None:
+            kwargs.pop("max_iterations")
         for problem in problems.values():
             logger.info(f"Solving problem {problem}.")
             _ = problem.solve(**kwargs)
diff --git a/src/moscot/problems/cross_modality/_translation.py b/src/moscot/problems/cross_modality/_translation.py
index ff91f015..693058c7 100644
--- a/src/moscot/problems/cross_modality/_translation.py
+++ b/src/moscot/problems/cross_modality/_translation.py
@@ -192,8 +192,8 @@ def solve(  # type: ignore[override]
         initializer: QuadInitializer_t = None,
         initializer_kwargs: Mapping[str, Any] = types.MappingProxyType({}),
         jit: bool = True,
-        min_iterations: int = 5,
-        max_iterations: int = 50,
+        min_iterations: Optional[int] = None,
+        max_iterations: Optional[int] = None,
         threshold: float = 1e-3,
         linear_solver_kwargs: Mapping[str, Any] = types.MappingProxyType({}),
         device: Optional[Literal["cpu", "gpu", "tpu"]] = None,
diff --git a/src/moscot/problems/generic/_generic.py b/src/moscot/problems/generic/_generic.py
index 6f21cc96..1466aa99 100644
--- a/src/moscot/problems/generic/_generic.py
+++ b/src/moscot/problems/generic/_generic.py
@@ -147,8 +147,8 @@ def solve(
         threshold: float = 1e-3,
         lse_mode: bool = True,
         inner_iterations: int = 10,
-        min_iterations: int = 0,
-        max_iterations: int = 2000,
+        min_iterations: Optional[int] = None,
+        max_iterations: Optional[int] = None,
         device: Optional[Literal["cpu", "gpu", "tpu"]] = None,
         **kwargs: Any,
     ) -> "SinkhornProblem[K,B]":
@@ -373,8 +373,8 @@ def solve(
         initializer: QuadInitializer_t = None,
         initializer_kwargs: Mapping[str, Any] = types.MappingProxyType({}),
         jit: bool = True,
-        min_iterations: int = 5,
-        max_iterations: int = 50,
+        min_iterations: Optional[int] = None,
+        max_iterations: Optional[int] = None,
         threshold: float = 1e-3,
         linear_solver_kwargs: Mapping[str, Any] = types.MappingProxyType({}),
         device: Optional[Literal["cpu", "gpu", "tpu"]] = None,
@@ -604,8 +604,8 @@ def solve(
         initializer: QuadInitializer_t = None,
         initializer_kwargs: Mapping[str, Any] = types.MappingProxyType({}),
         jit: bool = True,
-        min_iterations: int = 5,
-        max_iterations: int = 50,
+        min_iterations: Optional[int] = None,
+        max_iterations: Optional[int] = None,
         threshold: float = 1e-3,
         linear_solver_kwargs: Mapping[str, Any] = types.MappingProxyType({}),
         device: Optional[Literal["cpu", "gpu", "tpu"]] = None,
diff --git a/src/moscot/problems/space/_alignment.py b/src/moscot/problems/space/_alignment.py
index 9d10f36e..f5a398d2 100644
--- a/src/moscot/problems/space/_alignment.py
+++ b/src/moscot/problems/space/_alignment.py
@@ -160,8 +160,8 @@ def solve(
         initializer: QuadInitializer_t = None,
         initializer_kwargs: Mapping[str, Any] = types.MappingProxyType({}),
         jit: bool = True,
-        min_iterations: int = 5,
-        max_iterations: int = 50,
+        min_iterations: Optional[int] = None,
+        max_iterations: Optional[int] = None,
         threshold: float = 1e-3,
         linear_solver_kwargs: Mapping[str, Any] = types.MappingProxyType({}),
         device: Optional[Literal["cpu", "gpu", "tpu"]] = None,
diff --git a/src/moscot/problems/space/_mapping.py b/src/moscot/problems/space/_mapping.py
index f98e20a5..f3243344 100644
--- a/src/moscot/problems/space/_mapping.py
+++ b/src/moscot/problems/space/_mapping.py
@@ -207,8 +207,8 @@ def solve(
         initializer: QuadInitializer_t = None,
         initializer_kwargs: Mapping[str, Any] = types.MappingProxyType({}),
         jit: bool = True,
-        min_iterations: int = 5,
-        max_iterations: int = 50,
+        min_iterations: Optional[int] = None,
+        max_iterations: Optional[int] = None,
         threshold: float = 1e-3,
         linear_solver_kwargs: Mapping[str, Any] = types.MappingProxyType({}),
         device: Optional[Literal["cpu", "gpu", "tpu"]] = None,
diff --git a/src/moscot/problems/spatiotemporal/_spatio_temporal.py b/src/moscot/problems/spatiotemporal/_spatio_temporal.py
index 7a80d97c..6a2e0424 100644
--- a/src/moscot/problems/spatiotemporal/_spatio_temporal.py
+++ b/src/moscot/problems/spatiotemporal/_spatio_temporal.py
@@ -174,8 +174,8 @@ def solve(
         initializer: QuadInitializer_t = None,
         initializer_kwargs: Mapping[str, Any] = types.MappingProxyType({}),
         jit: bool = True,
-        min_iterations: int = 5,
-        max_iterations: int = 50,
+        min_iterations: Optional[int] = None,
+        max_iterations: Optional[int] = None,
         threshold: float = 1e-3,
         linear_solver_kwargs: Mapping[str, Any] = types.MappingProxyType({}),
         device: Optional[Literal["cpu", "gpu", "tpu"]] = None,
diff --git a/src/moscot/problems/time/_lineage.py b/src/moscot/problems/time/_lineage.py
index 8c878e8d..fea290f4 100644
--- a/src/moscot/problems/time/_lineage.py
+++ b/src/moscot/problems/time/_lineage.py
@@ -160,8 +160,8 @@ def solve(
         threshold: float = 1e-3,
         lse_mode: bool = True,
         inner_iterations: int = 10,
-        min_iterations: int = 0,
-        max_iterations: int = 2000,
+        min_iterations: Optional[int] = None,
+        max_iterations: Optional[int] = None,
         device: Optional[Literal["cpu", "gpu", "tpu"]] = None,
         **kwargs: Any,
     ) -> "TemporalProblem":
@@ -406,8 +406,8 @@ def solve(
         initializer: QuadInitializer_t = None,
         initializer_kwargs: Mapping[str, Any] = types.MappingProxyType({}),
         jit: bool = True,
-        min_iterations: int = 5,
-        max_iterations: int = 50,
+        min_iterations: Optional[int] = None,
+        max_iterations: Optional[int] = None,
         threshold: float = 1e-3,
         linear_solver_kwargs: Mapping[str, Any] = types.MappingProxyType({}),
         device: Optional[Literal["cpu", "gpu", "tpu"]] = None,