diff --git a/src/intel/compiler/brw_nir_lower_cooperative_matrix.c b/src/intel/compiler/brw_nir_lower_cooperative_matrix.c
index cd75ceb0f1d..3577dc37baf 100644
--- a/src/intel/compiler/brw_nir_lower_cooperative_matrix.c
+++ b/src/intel/compiler/brw_nir_lower_cooperative_matrix.c
@@ -436,6 +436,76 @@ emit_packed_alu1(nir_builder *b,
    return nir_vec(b, results, dst_components);
 }
 
+static nir_op
+get_cmat_conversion_op(enum glsl_base_type src,
+                       enum glsl_base_type dst)
+{
+   if (src == GLSL_TYPE_BFLOAT16) {
+      assert(dst == GLSL_TYPE_FLOAT);
+      return nir_op_bf2f;
+
+   } else if (dst == GLSL_TYPE_BFLOAT16) {
+      assert(src == GLSL_TYPE_FLOAT);
+      return nir_op_f2bf;
+
+   } else {
+      return nir_type_conversion_op(nir_get_nir_type_for_glsl_base_type(src),
+                                    nir_get_nir_type_for_glsl_base_type(dst),
+                                    nir_rounding_mode_undef);
+   }
+}
+
+static void
+lower_cmat_convert(nir_builder *b, nir_intrinsic_instr *intrin,
+                   struct lower_cmat_state *state)
+{
+   nir_deref_instr *dst_slice = nir_src_as_deref(intrin->src[0]);
+   nir_deref_instr *src_slice = nir_src_as_deref(intrin->src[1]);
+
+   const slice_info *dst_info = get_slice_info(state, dst_slice);
+   const slice_info *src_info = get_slice_info(state, src_slice);
+
+   const nir_cmat_signed cmat_signed_mask = nir_intrinsic_cmat_signed_mask(intrin);
+
+   enum glsl_base_type src_element_type = glsl_apply_signedness_to_base_type(
+      src_info->desc.element_type, cmat_signed_mask & NIR_CMAT_A_SIGNED);
+   enum glsl_base_type dst_element_type = glsl_apply_signedness_to_base_type(
+      dst_info->desc.element_type, cmat_signed_mask & NIR_CMAT_RESULT_SIGNED);
+
+   bool needs_intermediate =
+      (src_element_type == GLSL_TYPE_BFLOAT16 && dst_element_type != GLSL_TYPE_FLOAT) ||
+      (src_element_type != GLSL_TYPE_FLOAT    && dst_element_type == GLSL_TYPE_BFLOAT16);
+
+   nir_def *result;
+   nir_def *src = nir_load_deref(b, src_slice);
+
+   if (needs_intermediate) {
+      /* Cooperative matrices must have the same "shape" to be converted. */
+      assert(src_info->desc.rows  == dst_info->desc.rows);
+      assert(src_info->desc.cols  == dst_info->desc.cols);
+      assert(src_info->desc.use   == dst_info->desc.use);
+      assert(src_info->desc.scope == dst_info->desc.scope);
+
+      struct glsl_cmat_description float_desc = src_info->desc;
+      float_desc.element_type = GLSL_TYPE_FLOAT;
+
+      slice_info float_info = {};
+      init_slice_info(state, float_desc, &float_info);
+
+      nir_op op1 = get_cmat_conversion_op(src_element_type, GLSL_TYPE_FLOAT);
+      nir_op op2 = get_cmat_conversion_op(GLSL_TYPE_FLOAT,  dst_element_type);
+
+      nir_def *tmp = emit_packed_alu1(b, state, src_info, &float_info, op1, src);
+      result = emit_packed_alu1(b, state, &float_info, dst_info, op2, tmp);
+
+   } else {
+      nir_op op = get_cmat_conversion_op(src_element_type, dst_element_type);
+      result = emit_packed_alu1(b, state, src_info, dst_info, op, src);
+   }
+
+   nir_store_deref(b, dst_slice, result, nir_component_mask(result->num_components));
+}
+
 static void
 lower_cmat_unary_op(nir_builder *b, nir_intrinsic_instr *intrin,
                     struct lower_cmat_state *state)
@@ -445,29 +515,10 @@ lower_cmat_unary_op(nir_builder *b, nir_intrinsic_instr *intrin,
 
    const slice_info *dst_info = get_slice_info(state, dst_slice);
    const slice_info *src_info = get_slice_info(state, src_slice);
+   assert(cmat_descriptions_are_equal(src_info->desc, dst_info->desc));
 
-   /* The type of the returned slice may be different from the type of the
-    * input slice if this is a convert operation.
-    */
-
-   nir_op op;
-
-   if (intrin->intrinsic == nir_intrinsic_cmat_unary_op) {
-      op = nir_intrinsic_alu_op(intrin);
-   } else {
-      const nir_cmat_signed cmat_signed_mask = nir_intrinsic_cmat_signed_mask(intrin);
-
-      enum glsl_base_type src_base_type = glsl_apply_signedness_to_base_type(
-         src_info->desc.element_type, cmat_signed_mask & NIR_CMAT_A_SIGNED);
-      enum glsl_base_type dst_base_type = glsl_apply_signedness_to_base_type(
-         dst_info->desc.element_type, cmat_signed_mask & NIR_CMAT_RESULT_SIGNED);
-
-      op = nir_type_conversion_op(nir_get_nir_type_for_glsl_base_type(src_base_type),
-                                  nir_get_nir_type_for_glsl_base_type(dst_base_type),
-                                  nir_rounding_mode_undef);
-   }
-
-   nir_def *result = emit_packed_alu1(b, state, src_info, dst_info, op,
+   nir_def *result = emit_packed_alu1(b, state, src_info, dst_info,
+                                      nir_intrinsic_alu_op(intrin),
                                       nir_load_deref(b, src_slice));
 
    nir_store_deref(b, dst_slice, result, nir_component_mask(result->num_components));
@@ -599,6 +650,9 @@ lower_cmat_instr(nir_builder *b, nir_instr *instr, void *_state)
    }
 
    case nir_intrinsic_cmat_convert:
+      lower_cmat_convert(b, intrin, state);
+      return NIR_LOWER_INSTR_PROGRESS_REPLACE;
+
    case nir_intrinsic_cmat_unary_op:
       lower_cmat_unary_op(b, intrin, state);
       return NIR_LOWER_INSTR_PROGRESS_REPLACE;