diff --git a/src/InferArguments.cpp b/src/InferArguments.cpp
index d2f55b1fa781..9fabb47b9ef8 100644
--- a/src/InferArguments.cpp
+++ b/src/InferArguments.cpp
@@ -5,6 +5,7 @@
 
 #include "ExternFuncArgument.h"
 #include "Function.h"
+#include "IROperator.h"
 #include "IRVisitor.h"
 #include "InferArguments.h"
 
@@ -197,7 +198,9 @@ class InferArguments : public IRGraphVisitor {
 
         ArgumentEstimates argument_estimates = p.get_argument_estimates();
         if (!p.is_buffer()) {
-            argument_estimates.scalar_def = p.scalar_expr();
+            // We don't want to crater here if a scalar param isn't set;
+            // instead, default to a zero of the right type, like we used to.
+            argument_estimates.scalar_def = p.has_scalar_expr() ? p.scalar_expr() : make_zero(p.type());
             argument_estimates.scalar_min = p.min_value();
             argument_estimates.scalar_max = p.max_value();
             argument_estimates.scalar_estimate = p.estimate();
diff --git a/src/Parameter.cpp b/src/Parameter.cpp
index 1155d5468f30..f3455c699f47 100644
--- a/src/Parameter.cpp
+++ b/src/Parameter.cpp
@@ -20,6 +20,7 @@ struct ParameterContents {
     std::vector<BufferConstraint> buffer_constraints;
     Expr scalar_default, scalar_min, scalar_max, scalar_estimate;
     const bool is_buffer;
+    bool data_ever_set = false;
     MemoryType memory_type = MemoryType::Auto;
 
     ParameterContents(Type t, bool b, int d, const std::string &n)
@@ -46,6 +47,10 @@ void destroy<Halide::Internal::ParameterContents>(const ParameterContents *p) {
 
 }  // namespace Internal
 
+void Parameter::check_data_ever_set() const {
+    user_assert(contents->data_ever_set) << "Parameter " << name() << " has never had a scalar value set.\n";
+}
+
 void Parameter::check_defined() const {
     user_assert(defined()) << "Parameter is undefined\n";
 }
@@ -123,8 +128,14 @@ bool Parameter::is_buffer() const {
     return contents->is_buffer;
 }
 
+bool Parameter::has_scalar_expr() const {
+    return defined() && !contents->is_buffer && contents->data_ever_set;
+}
+
 Expr Parameter::scalar_expr() const {
     check_is_scalar();
+    // Redundant here, since every call to scalar<>() also checks this.
+    // check_data_ever_set();
     const Type t = type();
     if (t.is_float()) {
         switch (t.bits()) {
@@ -198,16 +209,31 @@ void Parameter::set_buffer(const Buffer<> &b) {
     contents->buffer = b;
 }
 
-void *Parameter::scalar_address() const {
+const void *Parameter::read_only_scalar_address() const {
     check_is_scalar();
+    // Code that calls this method is (presumably) going
+    // to read from the address, so complain if the scalar value
+    // has never been set.
+    check_data_ever_set();
     return &contents->data;
 }
 
 uint64_t Parameter::scalar_raw_value() const {
     check_is_scalar();
+    check_data_ever_set();
     return contents->data;
 }
 
+void Parameter::set_scalar(const Type &val_type, halide_scalar_value_t val) {
+    check_type(val_type);
+    // Setting this to zero isn't strictly necessary, but it does
+    // mean that the 'unused' bits of the field are never affected by what
+    // may have previously been there.
+    contents->data = 0;
+    memcpy(&contents->data, &val, val_type.bytes());
+    contents->data_ever_set = true;
+}
+
 /** Tests if this handle is the same as another handle */
 bool Parameter::same_as(const Parameter &other) const {
     return contents.same_as(other.contents);
diff --git a/src/Parameter.h b/src/Parameter.h
index 712380c2576e..424555ed9253 100644
--- a/src/Parameter.h
+++ b/src/Parameter.h
@@ -35,6 +35,7 @@ struct ParameterContents;
 /** A reference-counted handle to a parameter to a halide
  * pipeline. May be a scalar parameter or a buffer */
 class Parameter {
+    void check_data_ever_set() const;
     void check_defined() const;
     void check_is_buffer() const;
     void check_is_scalar() const;
@@ -54,8 +55,9 @@ class Parameter {
 
     /** Get the pointer to the current value of the scalar
      * parameter. For a given parameter, this address will never
-     * change. Only relevant when jitting. */
-    void *scalar_address() const;
+     * change. Note that this can only be used to *read* from -- it must
+     * not be written to, so don't cast away the constness. Only relevant when jitting. */
+    const void *read_only_scalar_address() const;
 
     /** Get the raw data of the current value of the scalar
      * parameter. Only relevant when serializing. */
@@ -112,27 +114,30 @@ class Parameter {
     template<typename T>
     HALIDE_NO_USER_CODE_INLINE T scalar() const {
         check_type(type_of<T>());
-        return *((const T *)(scalar_address()));
+        check_data_ever_set();
+        return *((const T *)(read_only_scalar_address()));
     }
 
     /** This returns the current value of scalar<type()>()
-     * as an Expr. */
+     * as an Expr. If no value has ever been set, it will assert-fail */
     Expr scalar_expr() const;
 
+    /** This returns true if scalar_expr() would return a valid Expr,
+     * false if not. */
+    bool has_scalar_expr() const;
+
     /** If the parameter is a scalar parameter, set its current
      * value. Only relevant when jitting */
     template<typename T>
     HALIDE_NO_USER_CODE_INLINE void set_scalar(T val) {
-        check_type(type_of<T>());
-        *((T *)(scalar_address())) = val;
+        halide_scalar_value_t sv;
+        memcpy(&sv, &val, sizeof(val));
+        set_scalar(type_of<T>(), sv);
     }
 
     /** If the parameter is a scalar parameter, set its current
      * value. Only relevant when jitting */
-    HALIDE_NO_USER_CODE_INLINE void set_scalar(const Type &val_type, halide_scalar_value_t val) {
-        check_type(val_type);
-        memcpy(scalar_address(), &val, val_type.bytes());
-    }
+    void set_scalar(const Type &val_type, halide_scalar_value_t val);
 
     /** If the parameter is a buffer parameter, get its currently
      * bound buffer. Only relevant when jitting */
diff --git a/src/Pipeline.cpp b/src/Pipeline.cpp
index d51438e275fe..631033404137 100644
--- a/src/Pipeline.cpp
+++ b/src/Pipeline.cpp
@@ -843,7 +843,7 @@ void Pipeline::prepare_jit_call_arguments(RealizationArg &outputs, const Target
                     }
                     debug(2) << "JIT input ImageParam argument ";
                 } else {
-                    args_result.store[arg_index++] = p.scalar_address();
+                    args_result.store[arg_index++] = p.read_only_scalar_address();
                     debug(2) << "JIT input scalar argument ";
                 }
             }
diff --git a/test/error/CMakeLists.txt b/test/error/CMakeLists.txt
index 6e69490657f5..69e0979163b5 100644
--- a/test/error/CMakeLists.txt
+++ b/test/error/CMakeLists.txt
@@ -107,6 +107,7 @@ tests(GROUPS error
       undefined_pipeline_compile.cpp
       undefined_pipeline_realize.cpp
       undefined_rdom_dimension.cpp
+      uninitialized_param.cpp
       unknown_target.cpp
       vector_tile.cpp
       vectorize_dynamic.cpp
diff --git a/test/error/uninitialized_param.cpp b/test/error/uninitialized_param.cpp
new file mode 100644
index 000000000000..2fa8d47b2ec3
--- /dev/null
+++ b/test/error/uninitialized_param.cpp
@@ -0,0 +1,22 @@
+#include "Halide.h"
+#include <stdio.h>
+
+using namespace Halide;
+
+int main(int argc, char **argv) {
+    ImageParam image_param(Int(32), 2, "image_param");
+    Param<int> scalar_param("scalar_param");
+
+    Var x("x"), y("y");
+    Func f("f");
+
+    f(x, y) = image_param(x, y) + scalar_param;
+
+    Buffer<int> b(10, 10);
+    image_param.set(b);
+
+    f.realize({10, 10});
+
+    printf("Success!\n");
+    return 0;
+}