diff --git a/petab/v2/C.py b/petab/v2/C.py
index c94a1d29..b5325ff4 100644
--- a/petab/v2/C.py
+++ b/petab/v2/C.py
@@ -79,14 +79,10 @@
 NOMINAL_VALUE = "nominalValue"
 #: Estimate column in the parameter table
 ESTIMATE = "estimate"
-#: Initialization prior type column in the parameter table
-INITIALIZATION_PRIOR_TYPE = "initializationPriorType"
-#: Initialization prior parameters column in the parameter table
-INITIALIZATION_PRIOR_PARAMETERS = "initializationPriorParameters"
-#: Objective prior type column in the parameter table
-OBJECTIVE_PRIOR_TYPE = "objectivePriorType"
-#: Objective prior parameters column in the parameter table
-OBJECTIVE_PRIOR_PARAMETERS = "objectivePriorParameters"
+#: Prior distribution type column in the parameter table
+PRIOR_DISTRIBUTION = "priorDistribution"
+#: Prior parameters column in the parameter table
+PRIOR_PARAMETERS = "priorParameters"
 
 #: Mandatory columns of parameter table
 PARAMETER_DF_REQUIRED_COLS = [
@@ -101,10 +97,8 @@
 PARAMETER_DF_OPTIONAL_COLS = [
     PARAMETER_NAME,
     NOMINAL_VALUE,
-    INITIALIZATION_PRIOR_TYPE,
-    INITIALIZATION_PRIOR_PARAMETERS,
-    OBJECTIVE_PRIOR_TYPE,
-    OBJECTIVE_PRIOR_PARAMETERS,
+    PRIOR_DISTRIBUTION,
+    PRIOR_PARAMETERS,
 ]
 
 #: Parameter table columns
@@ -193,35 +187,50 @@
 
 # NOISE MODELS
 
-#: Uniform distribution
-UNIFORM = "uniform"
-#: Uniform distribution on the parameter scale
-PARAMETER_SCALE_UNIFORM = "parameterScaleUniform"
-#: Normal distribution
-NORMAL = "normal"
-#: Normal distribution on the parameter scale
-PARAMETER_SCALE_NORMAL = "parameterScaleNormal"
+
+#: Cauchy distribution.
+CAUCHY = "cauchy"
+#: Chi-squared distribution.
+# FIXME: "chisquare" in PEtab and sbml-distrib, but usually "chi-squared"
+CHI_SQUARED = "chisquare"
+#: Exponential distribution.
+EXPONENTIAL = "exponential"
+#: Gamma distribution.
+GAMMA = "gamma"
 #: Laplace distribution
 LAPLACE = "laplace"
-#: Laplace distribution on the parameter scale
-PARAMETER_SCALE_LAPLACE = "parameterScaleLaplace"
-#: Log-normal distribution
-LOG_NORMAL = "logNormal"
+#: Log10-normal distribution.
+LOG10_NORMAL = "log10-normal"
 #: Log-Laplace distribution
-LOG_LAPLACE = "logLaplace"
+LOG_LAPLACE = "log-laplace"
+#: Log-normal distribution
+LOG_NORMAL = "log-normal"
+#: Log-uniform distribution.
+LOG_UNIFORM = "log-uniform"
+#: Normal distribution
+NORMAL = "normal"
+#: Rayleigh distribution.
+RAYLEIGH = "rayleigh"
+#: Uniform distribution
+UNIFORM = "uniform"
 
-#: Supported prior types
-PRIOR_TYPES = [
-    UNIFORM,
-    NORMAL,
+#: Supported prior distribution types
+PRIOR_DISTRIBUTIONS = [
+    CAUCHY,
+    CHI_SQUARED,
+    EXPONENTIAL,
+    GAMMA,
     LAPLACE,
-    LOG_NORMAL,
+    LOG10_NORMAL,
     LOG_LAPLACE,
-    PARAMETER_SCALE_UNIFORM,
-    PARAMETER_SCALE_NORMAL,
-    PARAMETER_SCALE_LAPLACE,
+    LOG_NORMAL,
+    LOG_UNIFORM,
+    NORMAL,
+    RAYLEIGH,
+    UNIFORM,
 ]
 
+
 #: Supported noise distributions
 NOISE_MODELS = [NORMAL, LAPLACE]
 
diff --git a/petab/v2/core.py b/petab/v2/core.py
index 41abfb36..e4bd4370 100644
--- a/petab/v2/core.py
+++ b/petab/v2/core.py
@@ -124,35 +124,41 @@ class NoiseDistribution(str, Enum):
     LAPLACE = C.LAPLACE
 
 
-class PriorType(str, Enum):
+class PriorDistribution(str, Enum):
     """Prior types.
 
     Prior types as used in the PEtab parameters table.
     """
 
-    #: Normal distribution.
-    NORMAL = C.NORMAL
+    #: Cauchy distribution.
+    CAUCHY = C.CAUCHY
+    #: Chi-squared distribution.
+    CHI_SQUARED = C.CHI_SQUARED
+    #: Exponential distribution.
+    EXPONENTIAL = C.EXPONENTIAL
+    #: Gamma distribution.
+    GAMMA = C.GAMMA
     #: Laplace distribution.
     LAPLACE = C.LAPLACE
-    #: Uniform distribution.
-    UNIFORM = C.UNIFORM
-    #: Log-normal distribution.
-    LOG_NORMAL = C.LOG_NORMAL
+    #: Log10-normal distribution.
+    LOG10_NORMAL = C.LOG10_NORMAL
     #: Log-Laplace distribution
     LOG_LAPLACE = C.LOG_LAPLACE
-    PARAMETER_SCALE_NORMAL = C.PARAMETER_SCALE_NORMAL
-    PARAMETER_SCALE_LAPLACE = C.PARAMETER_SCALE_LAPLACE
-    PARAMETER_SCALE_UNIFORM = C.PARAMETER_SCALE_UNIFORM
-
+    #: Log-normal distribution.
+    LOG_NORMAL = C.LOG_NORMAL
+    #: Log-uniform distribution.
+    LOG_UNIFORM = C.LOG_UNIFORM
+    #: Normal distribution.
+    NORMAL = C.NORMAL
+    #: Rayleigh distribution.
+    RAYLEIGH = C.RAYLEIGH
+    #: Uniform distribution.
+    UNIFORM = C.UNIFORM
 
-#: Objective prior types as used in the PEtab parameters table.
-ObjectivePriorType = PriorType
-#: Initialization prior types as used in the PEtab parameters table.
-InitializationPriorType = PriorType
 
-assert set(C.PRIOR_TYPES) == {e.value for e in ObjectivePriorType}, (
-    "ObjectivePriorType enum does not match C.PRIOR_TYPES: "
-    f"{set(C.PRIOR_TYPES)} vs { {e.value for e in ObjectivePriorType} }"
+assert set(C.PRIOR_DISTRIBUTIONS) == {e.value for e in PriorDistribution}, (
+    "PriorDistribution enum does not match C.PRIOR_DISTRIBUTIONS "
+    f"{set(C.PRIOR_DISTRIBUTIONS)} vs { {e.value for e in PriorDistribution} }"
 )
 
 
@@ -849,18 +855,16 @@ class Parameter(BaseModel):
     ub: float | None = Field(alias=C.UPPER_BOUND, default=None)
     #: Nominal value.
     nominal_value: float | None = Field(alias=C.NOMINAL_VALUE, default=None)
-    #: Parameter scale.
-    # TODO: keep or remove?
-    scale: ParameterScale = Field(
-        alias=C.PARAMETER_SCALE, default=ParameterScale.LIN
-    )
-    # TODO: change to bool in PEtab, or serialize as 0/1?
-    #  https://github.com/PEtab-dev/PEtab/discussions/610
     #: Is the parameter to be estimated?
     estimate: bool = Field(alias=C.ESTIMATE, default=True)
-
-    # TODO priors
-    #  pydantic vs. petab.v1.priors.Prior
+    #: Type of parameter prior distribution.
+    prior_distribution: PriorDistribution | None = Field(
+        alias=C.PRIOR_DISTRIBUTION, default=None
+    )
+    #: Prior distribution parameters.
+    prior_parameters: list[float] = Field(
+        alias=C.PRIOR_PARAMETERS, default_factory=list
+    )
 
     #: :meta private:
     model_config = ConfigDict(
@@ -879,13 +883,22 @@ def _validate_id(cls, v):
             raise ValueError(f"Invalid ID: {v}")
         return v
 
+    @field_validator("prior_parameters", mode="before")
+    @classmethod
+    def _validate_prior_parameters(cls, v):
+        if isinstance(v, str):
+            v = v.split(C.PARAMETER_SEPARATOR)
+        elif not isinstance(v, Sequence):
+            v = [v]
+
+        return [float(x) for x in v]
+
     @field_validator("estimate", mode="before")
     @classmethod
     def _validate_estimate_before(cls, v):
         if isinstance(v, bool):
             return v
 
-        # TODO: clarify whether extra whitespace is allowed
         if isinstance(v, str):
             v = v.strip().lower()
             if v == "true":
@@ -929,8 +942,6 @@ def _validate(self) -> Self:
         ):
             raise ValueError("Lower bound must be less than upper bound.")
 
-        # TODO parameterScale?
-
         # TODO priorType, priorParameters
 
         return self
diff --git a/petab/v2/problem.py b/petab/v2/problem.py
index c2a8a6fa..cf4dc430 100644
--- a/petab/v2/problem.py
+++ b/petab/v2/problem.py
@@ -813,14 +813,13 @@ def n_measurements(self) -> int:
         """Number of measurements."""
         return len(self.measurement_table.measurements)
 
-    # TODO: update after implementing priors in `Parameter`
     @property
     def n_priors(self) -> int:
         """Number of priors."""
-        if OBJECTIVE_PRIOR_PARAMETERS not in self.parameter_df:
-            return 0
-
-        return self.parameter_df[OBJECTIVE_PRIOR_PARAMETERS].notna().sum()
+        return sum(
+            p.prior_distribution is not None
+            for p in self.parameter_table.parameters
+        )
 
     def validate(
         self, validation_tasks: list[ValidationTask] = None
@@ -944,10 +943,8 @@ def add_parameter(
         scale: str = None,
         lb: Number = None,
         ub: Number = None,
-        init_prior_type: str = None,
-        init_prior_pars: str | Sequence = None,
-        obj_prior_type: str = None,
-        obj_prior_pars: str | Sequence = None,
+        prior_dist: str = None,
+        prior_pars: str | Sequence = None,
         **kwargs,
     ):
         """Add a parameter to the problem.
@@ -959,11 +956,8 @@ def add_parameter(
             scale: The parameter scale
             lb: The lower bound of the parameter
             ub: The upper bound of the parameter
-            init_prior_type: The type of the initialization prior distribution
-            init_prior_pars: The parameters of the initialization prior
-                distribution
-            obj_prior_type: The type of the objective prior distribution
-            obj_prior_pars: The parameters of the objective prior distribution
+            prior_dist: The type of the prior distribution
+            prior_pars: The parameters of the prior distribution
             kwargs: additional columns/values to add to the parameter table
         """
         record = {
@@ -979,22 +973,14 @@ def add_parameter(
             record[LOWER_BOUND] = lb
         if ub is not None:
             record[UPPER_BOUND] = ub
-        if init_prior_type is not None:
-            record[INITIALIZATION_PRIOR_TYPE] = init_prior_type
-        if init_prior_pars is not None:
-            if not isinstance(init_prior_pars, str):
-                init_prior_pars = PARAMETER_SEPARATOR.join(
-                    map(str, init_prior_pars)
-                )
-            record[INITIALIZATION_PRIOR_PARAMETERS] = init_prior_pars
-        if obj_prior_type is not None:
-            record[OBJECTIVE_PRIOR_TYPE] = obj_prior_type
-        if obj_prior_pars is not None:
-            if not isinstance(obj_prior_pars, str):
-                obj_prior_pars = PARAMETER_SEPARATOR.join(
-                    map(str, obj_prior_pars)
-                )
-            record[OBJECTIVE_PRIOR_PARAMETERS] = obj_prior_pars
+        if prior_dist is not None:
+            record[PRIOR_DISTRIBUTION] = prior_dist
+        if prior_pars is not None:
+            if isinstance(prior_pars, Sequence) and not isinstance(
+                prior_pars, str
+            ):
+                prior_pars = PARAMETER_SEPARATOR.join(map(str, prior_pars))
+            record[PRIOR_PARAMETERS] = prior_pars
         record.update(kwargs)
 
         self.parameter_table += core.Parameter(**record)
@@ -1132,7 +1118,8 @@ def model_dump(self, **kwargs) -> dict[str, Any]:
                          'id': 'par',
                          'lb': 0.0,
                          'nominal_value': None,
-                         'scale': <ParameterScale.LIN: 'lin'>,
+                         'prior_distribution': None,
+                         'prior_parameters': [],
                          'ub': 1.0}]}
         """
         res = {